Honestly, if I'm not at least passably good at a game I can't enjoy it.
Seems to be my case too. I suck at RTS's and bullet-hell games, and I don't particularly like playing them either. Pretty much anything where I need to keep track of lots of things and react in real time I'm no good at.
I'm trying to change that! I'm starting to feel that's actually a pretty important topic. I'm starting to get used to games where I can just burn through without REALLY having to use. Semi-intelligent but relatively obvious strategies are usually enough. If they're not, I tend to get frustrated and quit. Of course, this holds mostly for strategy games.
But is that really the best way to approach games? If the new XCOM showed me anything, it was that losing CAN be fun, and it can be fun to struggle. I'd actually argue that it should be fun and that we should embrace it. It makes us re-think, re-evaluate, re-strategise. These are all things which are important. We should consider it a challenge rather than a failure. Facing challenges is part of life, and a very valuable skill...
I have huge difficulty in doing this still, but I am getting better. I take a deep breath, pause the game (if possible) and really rethink all cause-effect relationships that might be affecting what I'm doing. I concede territory to regroup... that kind of stuff!
For the less strategic and more dexterity-based games I sort of feel everyone has some natural limitations, but that by making a conscious effort to improve you can actually go pretty far. The same think I did before actually still happens, but more at the micro level... trying to understand exactly where you are failing and why, and where you need to press what key. I dunno. Less experience here