How does the arm wrestling tournament represet what Rutherford found out about the positive and negative charges and atom

In the arm wrestling tournament each opponent is trying to pin down the arm of the other. Similarly, in an atom if there were only electrons or only protons they would each repeal the other very strongly. This is because like charges repeal each other.

But if there are both equally strong arm wrestlers then one will not be able to defeat the other. In the same way atoms have equal number of protons and electrons which strongly attract each other. Thus stabilizing the atom.