I actually kind of like roll-under, although I rarely get to play in systems that use it (I really want to play Dragonbane, and I have played a lot of GURPS, and one CoC game). However, I can see some "problems" with it that could bother people.
One, as people have mentioned elsewhere in this thread is that modifiers are not always intuitive. A "-3 bonus" is a bit counterintuitive, since we're primed to seeing minuses as negatives and therefore bad. A "+2 penalty" is just as confusing. And as people have said elsewhere in this thread, some games, like AD&D, were very random about how they wrote things. So something might give a +3 bonus, but that actually means subtract 3, but it could also mean the writer always adds 3 to the number they're rolling under--it results in the same thing, but it has a different feel to it. And worse, the writer may not have added the words bonus or penalty, which causes the reader to take an extra second to parse its meaning.
Two, in some games, especially some of the OSR games I've seen where you both roll under your stat for everything and the stats are rolled 3d6, it's pretty easy to fail at early levels. Or even at higher levels, since a lot of those games don't let you easily increase your stats. With a roll-over system, you can set the DCs low enough that low-level characters with middling stats are still likely to succeed at least some of the time. But with roll-under-the-stat system, you may have a stat of 6 or lower, and that's far more likely to fail.
Three, many people like big numbers. You don't really get those in roll-under systems, unless you're using d%s.
These issues can be mitigated by always being consistent with terminology and using point-buy or a basic starting level for your stats like GURPS does, or by being free with bonuses to rolls rather than sticking the rules to them in a little section off to the side.