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.
In 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. There is often an underlying slight anxiety between human and cat because of the large size difference. That is a personal view.
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. 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 he understand that.