How is it that an electron accelerates towards the protons (nucleus) in a hydrogen atom?

I had thought that the electric forces acting on each other is equal so they are in equilibrium.

The force of item 1 on item 2 is equal and opposite to the force of item 2 on item 1.

But you are only concerned with the forces on the electron (item 1) in this case. There is only one such force and it is NOT cancelled out.