I can't agree with this as a general rule. There are plenty of people who, when I was a teenager, I thought they were dumb and that did not change just because I became an adult. It depends on both the teenager and the adult, although, I'd say it is more about the teenager than the adult.
There are lots of teenagers out there that are quite intelligent, very observant, and highly respectful of any adult that deserves it. We hear more about and seem to notice more often those teens that do act immature and disrespectful of adults because it is human nature to ignore that which is going right and notice what is going wrong.
There are a lot of adults out there who think they know more than they do (even ones who are teachers) and/or have a lot of biases. I had a teacher in high school who should not have been an English teacher. I know that at 16 I was smarter than her. I was respectful to her in class and around other students (with the exception of my best friend in private), but that was how I was raised. I have had several teachers who did not know how to teach well, they just put out the material or gave an assignment without being willing or able to help the students with any problems. The issues arise when a teenager is disrespectful to teachers, whether the teacher is a good teacher or a bad one. Problems with teachers that will actually affect a students learning should be dealt with through a student's parents or other adults, not complained about/brought up in front of other students. And there are a lot of teenagers out there that do know this and do this, they just don't get recognition for it because it is the right thing to do.
Also, I consider my father an idiot with very little common sense, and I am 30. He has a lot of (useless) knowledge and he is a nice guy, but he hasn't gotten any smarter to me with age. Especially not since he left my mother. I think of my mother as a hardworking, intelligent, responsible woman, but I have thought of her that way since before high school.