I’m struggling to understand why a negative voltage applied to the bulk contact of an n-type MOSFET increases the threshold voltage. I can see why it happens due to the equations, but I can’t wrap my head around how it actually works.

I have 2 questions:

1. Applying a negative voltage to the bulk makes the potential difference (and thus the field?) between the gate and the bulk greater, which should make it easier to attract electrons under the gate. Why is this wrong?

2. Intuitively, the negative voltage at the bulk terminal repels electrons, pushing them towards the gate. Doesn’t this mean that the electron concentration under the gate increases more rapidly, reducing the threshold voltage?

Edit after John's answer:

Thank you, I think I get it now, but what would happen if we instead considered an MOS capacitor, so with no n+ doped regions? There I can't see how the threshold would increase.