I wish that I could give a really straightforward answer for this question, but it's not possible.
The quote that is listed does not appear in Jon Krakauer's book Into the Wild. The quote listed in this question is taken from the script of the 2007 film Into the Wild. The film was directed by Sean Penn, and the screenplay was also written by Sean Penn. In the movie version, McCandless says the above quote to Ron Franz. There is a similar quote in the book.
Early in his senior year at Woodson, Chris informed his parents that he had no intention of going to college. When Walt and Billie suggested that he needed a college degree to attain a fulfilling career, Chris answered that careers were demeaning “twentieth-century inventions,” more of a liability than an asset, and that he would do fine without one, thank you.
The above text can be found on page 71 of my version. McCandless isn't talking to Franz though. He's talking to his family about his desire to live life on the road and in the moment. McCandless's decision is a big blow to his family because they see education and good careers as very important.
“That put us into kind of a tizzy,” Walt admits.
In the book, Franz does attempt to get McCandless back on track for a "normal" life, but McCandless politely explains his attitude.
When he returned to McCandless’s camp and launched into the self improvement pitch, though, McCandless cut him off abruptly. “Look, Mr. Franz,” he declared, “you don’t need to worry about me. I have a college education. I’m not destitute. I’m living like this by choice.”
Sean Penn's film combined the conversation between Franz and McCandless with the conversation between McCandless and his parents. It makes sense that Penn did this because even Krakauer hints that Franz and McCandless shared a closeness that McCandless didn't have with his parents.