It will depend on the animal. I train my dogs from pups to let me handle them in any way I need to. I can do whatever I need to to check their paws....and they love it! They get a nice leg massage after I am done feeling around the pads for anything that should not be there.
Because they're afraid you have germs and they have no place to carry hand sanitizer? LOL I'm just SO kidding, sweetheart. That's a very good question and have wondered it myself for years. I'm old and I've had dogs (and I hate calling them that 'cause they're my babies) all my life, but have only had one that didn't mind for me to touch his paws. I'm anxious to see the answers you get. I wish a vet would answer! It seems that all of them are that way. It's like I've never known a cat that liked to be scratched from back to front. Little idiosyncracies like that are amazing! Have a wonderful night, Tiffany!