I'm definitely not going to disagree with this, but there's also a lot to be said for age and experience when it comes to understanding things. Being exposed to it once starts you off, but even if you don't think about or work at it consciously, the second time -- particularly years later -- unless you've been living under a rock, you're likely to see a massive improvement in your understanding right off the bat.

This is particularly true when you're still working your way through school. That time is more dense with learning about learning than any other time you're likely to spend; it's not something you might be concentrating on intentionally, but building up your abilities and knowledge result in the way and speed at which you learn changing and improving.

Like I said, I'm not denigrating teaching or its positive effects in this vein at all. But there's also something else (at least one something) at work here that might be playing a larger role than realized.