Bernoulli's Principle conceptual question

So, I understand that for a fluid flowing (in a pipe, for example), an area decrease between points 1 and 2 results in a velocity increase. I also understand that this velocity increase is a result of flow rate being constant and/or a lower pressure at point 2 (causing the higher pressure at point 1 to kind of push the fluid faster). However, if I look at it from the view of P = F/A, then shouldn't an area decrease mean a pressure increase? I have a feeling that I'm just missing something very simple, so I would love help. Thank you.

You cant use P = F/A in this case, because the force changes, it's the flow rate that is constant. Does that solve it for you? if you look at the picture on the wikipedia site below, i make sense of it like this;
on the big side of the horizontal tube, the fluid is forced through a small hole resulting in a pressure (and force) increase. Because the fluid does not meet any additional obstructions in the small end of the tube, the pressure is lower at that side, because it can go straight ahead with little problem.

It is a Conservation of Energy calculation

Energy of flowing fluid has 3 components

Pressure energy + potential energy + kinetic energy = constant

For level pipe, elevation does not change so the potential energy is constant. That means if kinetic energy increases then pressure energy must decrease (pressure decreases)

By conservation of mass the same amount of mass passes through a cross section per unit time for incompressible flow. So, if cross section decreases then velocity increases so KE increases so pressure must decrease