Why can’t we look at the trabecular meshwork directly?

Because of total internal reflection. Light from the trabecular meshwork moves toward the cornea, but reflects back into the eye at the tear-film-air interface. This has to do with Snell’s Law and the way light bends when going from a high-density medium into air.

You can see this same phenomenon when swimming underwater. If you look straight up, you can see the sky above you. But if you look more tangentially, the under surface of the water turns into a mirror.

We can break this reflection by interrupting the tear-air interface. A gonio-prism is glass contact lens with a prism that it pressed against the cornea and allows us to see into the angle.