The important stuff I learned before graduating my bachelors was things like:
1) It's better to be a small fish in the big pond (my career councillor told me this when I was 16, I think I disagreed with it in my first 3 years of uni but now I can totally agree.)
2) You don't owe anyone anything and you aren't tied to anyplace on earth (Mum - grew up moving a lot so when I had an opportunity to attend a more prestigious university my mum gave me a lot of support)
3) Always swap jobs every few years (my uncle worked for the same company for 18 years before being laid off - he has done well but nearly everyone he started working with are execs now)
Most related to your comment is something I was told a few years after university where I was pushing work to fast track my professional development as much as possible. A senior manager told me there is only so much other people can teach you, in the end you need to do the time and build the experience.