Why do some teens ignore authority and then claim they aren't strong enough to ignore peer pressure?

Perhaps because the approval of peers means more to them than the approval of authority figures?

I hear a math teacher tell the story that he started his class one day by having students compute the percent of people in the room who were female. He did this in two classes, and in both instances the first student to give a response gave a wrong answer. Why? Because the student failed to count the teacher as a "person."

How can one respect the authority of someone who has been ob<x>jectified as a nonperson?

I believe it's because of some sort of unconscious thinking on how high up the ladder a person is. To a teen, the higher the person on the ladder, the higher (depending on the teen) chance of that teen being rebellious. People of their equal rank don't intimidate them as much, so they probably see it as "going with the flow"
Or at least that's my idea owo

It's the "teeny bloopers" that think that ;) Definitely not hating; Jus saying .... My teeny boppers are cool though :)

their frontal cortex isnt fully formed so cause and effect have really no relevance to them they just do what feels good at the time

Don't know. I guess teens don't connect the two :/ Most of them don't really "think" just do XD