Why does a black hole grow when it consumes matter? Isn't this a contradiction?

The density of a black hole is concentrated at the singularity at its center, where density becomes infinite and the Theory of Relativity breaks down. Although the Theory of Relativity is insufficient to describe what happens at the singularity, it may be assumed that the density at that point can not increase. Therefore, accretion of matter does not increase the density at the singularity, but rather increases the Schwarzschild radius of the black hole, expanding the event horizon. Gravity increases, but so does the size of the black hole.

Surely then, if a black hole consumes more mass, therefore it's gravity would be greater and thus exert a greater force on the light, pulling it tighter, resulting in a smaller black hole...

To use your logic, if the gravity is stronger, then things (and light) farther away that used to not be trapped can now be trapped by the stronger gravity, hence that boundary between where things are trapped and where things aren't trapped is now farther out, and that's the size of the black hole, so the size is larger.

There is a still a potential hole in your argument however. Which is that you just assumed the black hole could consume things. But if something happens it is reasonable to ask when and where it happened, which is a hard thing to answer for a black hole.

People on the outside never see a black hole form and they never see a black hole consume something. They see stuff that starts to look more and more like a black bole as time goes on. And they see new stuff join up and the new larger collection start to look more and more like a black hole.

This is basically because of extreme time dilation between the forming surface and the outside where we see the things near the forming surface going slowly.

And if it is an astrophysical black hole, there isn't even a surface we just see the original matter say the neutron star collapsing in slower and slower slow motion and getting redder and redder.

Surely then, if a black hole consumes more mass, therefore it's gravity would be greater and thus exert a greater force on the light, pulling it tighter, resulting in a smaller black hole...

Define size of a black hole:

The Schwarzschild radius :

The Schwarzschild radius (event horizon) just marks the radius of a sphere past which we can get no particles, no light, no information.

Note that the radius, which defines the volume from which there is no return, is proportional to the mass, so the larger the mass the larger the volume of the black hole trap.

Your misunderstanding comes from "pulling it tighter". The strength of the gravitational field of the larger in mass black hole extends further then when it was smaller in mass.

The size of the blackhole (i.e. its blackness) is not its actual size. It is the area where light simply cannot escape. The more mass the blackhole gets, the wider this area be due to increased gravity pull. It's actual size? We do not know but it is assumed as a singularity at its center.