My cat seems to dislike me holding her front paws, although my friend's cat doesn't seem to mind. Is this problem specific to my cat or does it apply to the general population of cats?
The biggest reason I can think of is that you're taking away a defence mechanism for the cat. Is your friends' cat declawed by any chance? If it is, it may be that it no longer sees those paws a defence. In general, though, I've found that cats see that as an aggressive behavior and react (mine will nip if I do it).
Cats don't usually like to have their paws held, touched, or anything like that. If they are in a mellow mood and trust you they might not mind as much. My "grrrls" tend not to mind me gently petting their front paws, but the ones I've had longer (and bonded more with) are more tolerant of it. Paws are a sensitive area that they depend on and having a paw held probably seems instinctively "wrong" and "dangerous" to them. They could view it as seriously limiting their mobility. They have a similar mentality with having their belly petted (a cat who trusts you and is in a mellow mood might let you do it, but otherwise they might get angry) as it is a "weak spot".
I would never do this myself but I did observe (when I was younger) someone put bags on their cats feet (with rubber bands). The cat was so disturbed about having the bags on its feet it incessantly walked backwards to try to get its paws out of the bags. Do not do this as it psychologically cruel to them.
"You're doing what to me?" ... Think of it as being ticklish. The cat doesn't know whether you're offering foot massage, are about to clip its claws, or are just being weird, and nobody likes not knowing what's going on and how they should react.
With patience you can convince many cats to accept this, if you give them clear signals that you're just grooming their feet. Expect it to be a multi-year campaign, unless you're willing to resort to bribery (treat training).
I acclimate my cats to this, to having their ears examined, and to a few other indignities as caresses quite deliberately, so they'll be more tolerant when I need to examine or treat them medically. I should put tooth-cleaning and examination on that list too.