Again I did see these arguments before and mostly from people who seem nothing more than sexist pigs at times.
Really there is a lot of sexist undertones in some comments I read and heard and please note I am not calling folks here sexist as at least while most of the arguments I heard before seem more refined and less like an angry rant by some loser who lives in their mothers basement.
Might have to ask yourself then if you dislike the argument or the source on this. I can do a comparison between SAO's Kirito and Rey or Deathmarch's Sato and Rey or the protagonist of "in another world with my smartphone" and Rey if you need me to prove my basis that this is about the presentation and not the gender.
(BTW: I am actually proud of myself that I have forgotten the name of Smartphone's protagonist. It's something I'd rather not remember. So, actually, please do not make me run a comparison between Rey and that guy. I will have to use mind bleach afterward just to remove the trauma of looking at that bastard again.)
But I heard this too and I can counter it by saying we didn't see Luke training to use the force between ANH and ESB, plus he seemed very apt at piloting an X wing despite us not seeing him training how to use one.
2 things. 1, the ability Luke showed with the X-wing was actually kinda basic. He was not really put into position where he had to do any complex dogfighting and such. Nothing at all like Poe Dameron's single uninterrupted shot dogfight over that Mos-eyesly in the forest place in TFA. (The one that ended with the guy yelling "Woo! What a pilot!")
All Luke did was fly straight and get into the trench, and veer off when someone got on his tail as he tried to escape. We can probably safely presume he just got some rudimentary training on weapon systems and then mixed it with what he knew about piloting speeders to justify that. You have to keep in mind this was a bunch of rebels struggling for survival. Throwing a barely trained farmboy at the death star is exactly the kind of move they would pull in that situation.
This doesn't even compare to Rey piloting the falcon better than Han. It's all about points of comparison to judge skill scales. Rey shows way too much skill for the level of experience, training, and exposure she ought to have.
As for the force, the only thing he did before being sent to Degoba was try to force move his lightsaber stuck in the snow. Now, for the sake of being intellectually honest, I will grant you this one. He had never seen this as a potential possible move before he tried it. Obi-wan had never shown Luke force telekenisis. However, given the danger of his situation, we can excuse that one by assuming he was just desperately trying to reach his lightsaber in this urgent life-or-death situation and that triggered something. It can be seen as a clumsy move, and force telekenisis is a technique that is far more brute force compared to Jedi mind control.
Jedi mind control by comparison requires you to use the force while strongly implanting a hypnotic suggestion. A specific phrasing of words as you try to dominate the mind. That's something you actually have to know is possible before trying it, likely having seen someone else actually do it before.
I will still admit that we do not know the power or skill level necessary for each, so I am fine with setting the two techniques as equal on both skill and power level. However, the mind dominance skill is still something that requires you to actually know about it before trying it while telekenisis is something you can excuse as something you could accidentally use in a desperate enough situation. This being the case, we could just as easily chalk this one up to bad writing rather than anything else.
Bad writing is something rather consistent in the starwars sequel trilogy. The thing that is a lot less excusable is the part where the team is looking for her and they all basically go "there she is" as she has already rescued herself.
Basically, the entire point of that badly written scene was to demonstrate Rey using the force somehow, and they chose the worst force power to justify when they did it. Plot wise, it would have made just as much sense for her to get out of it by being rescued by the team. But, if you really don't like that, then a good alternative would be her being behind a forcefield and gets lucky because the guard is lazy and wanders off, figuring there's no problem because she's behind the forcefield. Then, she uses force telekenisis to flick the lever that controls the forcefield. That would have been quite a bit more acceptable.
Again, I am perfectly agreeable to chalking this one up to bad writing.
Also, we did see Kylo Ren was weakened by his fight with Fynn, and it did seem him killing Han effected him on an emotional level, so maybe he was not at his best with his first fight with Rey.
Rather than the argument of Rey being too skilled, I think the better argument here would be that Kylo is too conveniently unskilled compared to what he ought to be. I have actually done some traditional swordsmanship and am familiar with both Budo and HIMA. So, I can say that Darth Vader's technique is fairly spot on in Empire (Luke's is rather atrocious, but that kinda fits as well,) but ALL of the swordplay in the sequel trillogy is aweful, and it actually gets worse with each subsequent movie in the trilogy. It is barely passable in TFA, the throne room fightscene at the end of TLJ is the unholy love child between a **** show and a complete mess, and I can't speak on ROS because I never watched it.
(I do know she demonstrated force powers previously unseen in the Star Wars universe though, which is the single most unavoidably Mary Sue thing about her. Even that levitating while orbiting rocks around her thing in the trailers is way off the charts compared to previously established stuff.)
Anyway, I will give a little ground based on your justification, but at the end of the day it all boils down to this. You can justify Rey's victories all you want, but the real problem with her character is that she never really tastes failure. Nothing like what Luke got at the end of Empire. (Getting captured in TFA gets nullified by the fact she got out herself without assistance from anyone.)
At the very least, it's bad writing. The compounding of it all though adds up to this. She can do anything better than anybody and the one and only thing she is unable to do is fail. That makes her a Mary Sue.
I challenge you on this. Name one thing by the end of ROS that someone else can beat her at. Now, this was a rumor I heard, I will admit to that, but I heard that in ROS she demonstrates herself to be a better pilot than Poe. That one was the single last thing somebody else could have been better than her at. Even if it was down to just that one thing, in the sea of other things she was better than everyone else at she would have still qualified as a Mary Sue. The only thing taking away that one thing does is it removes the last shield defenders of Rey against the Mary Sue title could have hidden behind.
Again where is the training session for James Bond?
Or Luke for that matter between ANH and ESB?
How did he learn the Jedi Mind trick in ROTJ?
We never saw his training session on how to do it on camera, most of that is in the extended universe.
I mean can you see where I am getting at right?
I mentioned James Bond in a previous comment. He is an MI6 agent. Being an agent implies training previous to him being on camera. Rey was a scavanger on a desert planet. That means there is no room for implied training, and all the training she might have had needs to be specifically called out, mentioned, and justified because her background does not imply anything for her.
As for Luke, I already covered that. He had no real noticable jump in power between ANH and ESB, and the only move he did perform before getting training can be excused by the situation. As for the mind trick, we know he got training on Degobah and he did see Obi-wan use the mind trick. That's enough establishment for it to justify him using it. Force choke, which he also used in ROTJ, is only really an application of telekenisis.
All I said is that you need to justify the power and skill set. Training is only 1 form of justification. It's the most straight forward justification, but there are others. Most others don't really apply here though, it's things like Kriptonian DNA justifying Superman's powers. There are also situational justifications like what you did on arguing on the Kylo VS. Rey fight in TFA, or Luke being able to pull the lightsaber from the snow in ESB. Those are only 1 time justifications for single specific situations though, and it feels cheap and too coincidental if you keep giving situational justifications too often. Luke gets his situational justification record wiped when he gets thoroughly defeated at the end of ESB, and driven down to his lowest point. Rey never had a situation where she had a failure significant enough to clear her situational victory record. (That's really more writing than anything else though, but it still relates to how the fans perceive the character.)
At the end of the day though, some form of training is the thing that justifies things most effectively and in the most situations. Training can also be implied, such as the case of James Bond. In order to have the training be implied though, you need to actually credibly imply it. MI6 agent is a position where you would have to be an idiot to assume he got there without training, and there for his status as an MI6 agent does more than imply training. It actually makes it so you would have to show proof and justification in order to argue he didn't have training, just from hearing his affiliation.
Training under a teacher is not really necessary either, all having a master does is justify the training (yes, that's the thing about training. The justification itself also needs a justification (justifiception!)) Without the master to teach, you need to show where they would have gotten exposure to that skill to justify the self-training. With Rey being a scavanger, we could justify some implied self-training in identifying valuable parts, how to ration food, how to negotiate, and how to deal with street scum. Those four skills are very easily justified through implied self-training, but you need a little more justification to demonstrate ship repair and how to combat skilled soldiers. For example, this is another flaw in the writing. They could have actually very easily justified her ability to repair the Falcon if they just changed 1 thing and said Rey was trying to buy the falcon off the current owner in order to use it to get off the planet and had been running maintenance on it in preparation. Just that one bit of backstory would justify everything, and it could have just been a slipped in line. But, they didn't, and thus it's an unjustified skill.
Incredible talent is also a justification, but that only justifies quick learning or better results in self-training. They still need to have either exposure or be placed in a situation where you can say they would have picked up the skill out of necessity. If you are going the later route, you also need to either keep the skill to levels where it's believable given the situation or demonstrate other people were in that situation and responded to it in a similar way.
If you use the incredible talent justification, your character will be accused of being a Mary Sue unless you are extremely careful and put extra work into the justifications. Talent is one of those 1 step forward 2 steps back justifications where you actually need to try even harder as a writer to justify every single skill they pick up in order to avoid Mary Sue treatment for your character.
(An example of a character who pulled off the talent card right would be one of my absolute favorite characters. Rudeus Greyrat form Mushoku Tensei. He has talent, but every skill he has is justified through training that shows exactly step by step how he acquired it. Also, he fails constantly. Almost everything goes wrong for him in the short run, and he only just barely manages to keep everyone alive at the end of the day. He constantly tastes failure. And, he grows as a person for it. I would also like to add, I said Rudeus was my favorite character, not my favorite person. As a person, especially in the first half of the story, he's a disgusting pig. He's completely unlikeable. If he was a real person, I would want him nowhere near me. However, that is part of what makes him a good character. Being too perfect and without flaws that would turn you off of the person makes them inhuman, and also raises Mary Sue flags left and right. That's something to keep in mind about character flaws. If you are giving a character a flaw, it should not be something that makes them endearing. Endearing flaws are Mary Sue flaws. If you are going to give them a flaw, it should be something that would loose them friends in real life. Rudeus has a lot of those. Almost too many.)