Ground Wire is Turning on Light

I have been wiring a new room in my house. The room has its own dedicated circuit breaker. I have 10 receptacles and 4 recessed lights. The lights are controlled by 2 switches, one for each pair of lights.

I have a metal junction box that I use to hold the wires controlling the lights. I am using 12 romex( has 2 wires a bare copper ground wire). The wire coming into the box is my input and I will call it W1 ( has H1, N1 and G1). The wire coming out and feeding the light is W2( H2, N2 and G2). There is a third wire coming into the box from the switch S ( has S1 and S2).

Inside the box I have the following connections: H1+H2, G1 +G2, N1+S1, S2 +N2. The switch is controlling my neutral wire.

When I screwed a bulb into the light fixture, it came on even though the switch was off. I disconnected the switch and the light is still lit.

I discovered that the bare metal ground wire is touching the metal box. When I move the wire the light goes off. If I retouch the wire to the box it comes on.

This makes no sense to me at all. How is this light coming on when my neutral wire is effectively "cut" by not have any connection at all?