Particle decay has to conserve the various conserved quantities - energy, momentum, charge, lepton number, baryon number, etc....  So in this case, the important points are that a proton must decay into a final state that has a baryon (to conserve baryon number) and the mass of the final products must be less than the mass or the proton (to conserve energy).  Since the proton is the lightest baryon (just slightly lighter than the neutron), there isn't anything for it to decay into without violating either baryon number conservation or energy conservation.

I didn't check but I assume the proton half-life of 10^32 years is a lower limit from measurements. After reading the answer by JR Arrington I was wondering what are the theoretical backgrounds for questioning the stability of free protons?

In many cases, we observe that a certain quantity (e.g. Baryon number) is conserved, and we understand why this happens in the Standard Model.  But we also know that there are missing pieces in our understanding, physics beyond the Standard Model, which can violate certain symmetries or conservation laws. So looking for proton decay is a way of searching for new physics.  In the Standard Model, the proton cannot decay, and so any observation of proton decay is the signal of something new and exciting.

Cause the neutron have no charge equal zeroo therfore it's responsible about the nuclear fission by slow neutron