"That's what it says on the answer key."
I had a similar experience. These kinds of problems happen most often when it's either a departmentalized exam or the teacher is just pig-headed. The former happens because most often department head teachers don't check the answer keys properly, while the latter happens because there are teachers that are just like that~pig headed.
Honestly, if the teacher doesn't know their subject
In my opinion, that's no longer a teacher but a con artist. Hahaha... That teacher of yours though must be eager for retirement and doesn't care anymore about his/her students. What a waste of salary.
I went to a public school, so I can't really complain about whether the teacher knows his/her stuff. It's pretty much rough in my country. Educators complain that they don't have it easy because their students are turning the table against them thanks to the laws protecting them. That's why at some point, many teachers got infected with a disease that makes them lose their passion for teaching.