In case of solar system,we can explain "Why Sun would not revolve around any other planet?",by giving the reason that Sun is heavier than any other planets.
Heavier the body,greater will be the gravitational strength produced by it.Thus,Sun being heaviest,produces greater gravitational pull,and keeps other planets revolving around it.
In case of atom,we can consider coulomb's law.Here,we can see that both protons and electrons have same charge in magnitude(Don't consider electron to have less charge than proton,because of negative sign.It just implies that electron is resinously charged i.e charge similar to amber).
So,in case of atom we don't have electrons and proton with different charge in magnitude,as like we had Sun to be heavier than other planets,to make other planets to revolve around the sun.Thus,we can also expect protons to revolve around the electron.But,this doesn't happen.So,what is the reason for protons not revolving around the nucleus cotaining electrons and neutrons?.