This is actually more delicate than that. It is not possible to split a proton into its constituent quarks because quarks can never exist on their own. As far as we know they only appear in pairs or three at a time as in the proton.

There is also the issue of baryon number conservation. This is physical law (as far as we know) that says that the number of baryons must be constant. A proton is a baryon and neuron is a baryon but there are lots more. Anti-particles count negative so we can destroy a proton by combining it with an anti-proton, if we would happen to have one. But we cannot outright split the proton into some smaller set of parts as with an atom.