Gravity is the weakest of the fundamental forces, so what is so special about gravity that it can form an inescapably strong field while a force like the EM force cannot? It seems to me that if there were some extremely strong electric field, that it would only have an influence on particles that carry a charge, and so it would make sense that a black hole could not from from the EM force because it could not affect particles like neutrons. However, the same logic cannot be applied to black holes caused by gravity, because things like photons, which have no mass, still cannot escape the intense gravitational field. Why does gravity influence things that have no "gravitational charge" while the EM force cannot influence things that have no "electric charge." Because otherwise it would follow that a strong enough EM field should be fundamentally inescapable in the same way a black hole is inescapable. I know E=mc^2, so obviously a strong enough EM field would eventually act like a gravitational black hole, but why wouldn't it be easier for an EM black hole to form than a gravitational one since the EM force is so much stronger?
The forces other than gravitation include strong, electroweak, and electromagnetism. The first two could not produce a black hole because they are both very short range forces. Beyond dimensions much larger than an atomic nucleus, these effects (strong, electroweak) are negligible. Chiefly this is because the bosons that carry those forces soon decay into other particles outside of the range of atomic nuclei.
Coulomb forces (electromagnetic) do not create black holes for several reasons, but probably the best one is that a collection of like charges tend to repel each other, and mixed charges become electrically neutral outside of the scale of the atom (and thus are no longer able to attract additional charge of either sign, positive or negative.
The answer can be found in the nature of gravity. It is a force that arises due to curvature of spacetime which underlies everything. A black hole is a specific configuration of spacetime where nothing can leave by definition, not even light. Since there is no concept comparable to curved spacetime underlying the other forces, we observe no such phenomena.