It's true that there are some exemptions for "fair use" of copyrighted material for educational purposes, but there are details to be aware of and rules to follow. There is no difference between a TV series and general YouTube content in terms of requiring permission (or not, if it's fair use), they are both copyrighted.

You are more likely to get away with any copyright infringement of some random youtuber, than a commercial TV show, but only because the latter has a much greater economic interest, and money to pay lawyers to stop you.