Cats have a refined sense of touch. Their paw pads are extremely sensitive. They are packed with receptors which provide information on what is underneath their paws. Also their claws are packed with nerve endings. These nerves tell the cat how far each claw is extended and the amount of resistance the claw is experiencing.
When hunting, cats’ claws and paw pads send information to their brains on the how their prey is struggling to escape.
Cats’ canine teeth are also sensitive to touch. This allows cats to direct their killing bite more accurately between their preys’ vertebrae which kills prey almost painlessly and instantly.
Conclusion: the reason why cats dislike their paws being touch is probably because they are very sensitive. There may also be a secondary issue, namely, that when people touch their cat’s paws they tend to hold them which may make the cat feel that she is trapped. I find a cat is more likely to accept their paws being touched on the paw pads than on the top of the paw. This makes sense as the paw pads are constantly in contact with objects whereas the top of the paw should be free of all objects. I think that cats need that freedom to react quickly (constant alertness) if needs be and placing a finger or hand over their paw limits that sense of freedom. This alertness is apparent when they ‘sleep’. They can wake up and jump off in a second or two. Their ears are mobile when snoozing.
I also believe that there is often an underlying slight anxiety between human and cat because of the large size difference. This can make then cautious.
P.S. A person touching a cat’s paws is different to a cat extending his/her paw to touch their human companion. This is a gentle touch for making physical contact at the cat’s request. The article is about a person taking hold of a cat’s paws between thumb and finger or placing their finger or fingers on the paw. I often touch my cat’s paws but it a very gentle process and the signal I give my cat is that it is done in companionship and I believe that he understands that.