thought it had something to do with education

The title of the film "An Education" refers to her experiences with an older man and the realization that her formal schooling was limited. Remember, this is the memoir of a real person, even though the story is fictionalized. But it is very limited by the era in which these experiences occurred. The 1960's were a very very conservative time and, after glimpsing another life with David, Jenny reverts to who whe is: a teen girl of middle class parents in Britain who's smart enough to go to college.

If this movie had been set in the 70's or 80's it might have had a very different ending.

And your dream of life without the school system forcibly imprinted? Home schooling and self study is, was, and always has been a viable alternative.

From the original source (the main character's real name is actually Simon):

"What did I get from Simon? An education -- the thing my parents always wanted me to have... I learned about expensive restaurants and luxury hotels and foreign travel, I learned about antiques and Bergman films and classical music. But actually there was a much bigger bonus than that. My experience with Simon entirely cured my craving for sophistication. By the time I got to Oxford, I wanted nothing more than to meet kind, decent, straightforward boys my own age, no matter if they were gauche or virgins. I would marry one eventually and stay married all my life and for that, I suppose, I have Simon to thank."

Judging from your reply, looks like you could have used one.

It's an education, all right, the school of hard knocks variety. Jenny thought she was taking the path to something finer and more glamorous, and instead turned into a grifter who was being used by her man. But she at least learned from the experience.

The only thing the film got wrong, I think, was the very pat reversal at the end, where Jenny was able to gain back everything she'd thrown away. I'm glad things worked out for her, but it weakens the ending that there was no cost to her errant ways, beyond having to work hard.