No. Even degeneracy pressure from the Pauli exclusion principle has a limit; it can't hold an object up against gravity for an arbitrarily large mass. So neutron stars, like white dwarfs, have a maximum mass limit; any object over that mass cannot be a neutron star because neutron degeneracy pressure can't hold it up against its own gravity. (The article briefly mentions this; the limit is the Tolman-Oppenheimer-Volkoff limit.)

We don't know exactly what that maximum mass limit is for neutron stars, because we don't know their equation of state with sufficient accuracy (whereas we know the white dwarf equation of state accurately enough to know that the maximum mass limit for them is 1.4 times the mass of the Sun), but we know it's somewhere betweena about 2 and 3 times the mass of the Sun. Objects more massive than that can only be black holes.

As far as how black holes form, they form when a sufficiently massive object collapses under its own gravity. Usually this happens when a star runs out of nuclear fuel. (More precisely, this is how black holes of roughly stellar mass form. For supermassive holes, like the one at the center of our galaxy, things are more complicated, because they probably don't form in one single process, they form over a long period of time as a hole that started out a lot smaller swallows other massive objects.) If the collapsing object is over the maximum mass limit for a neutron star, degeneracy pressure from the Pauli exclusion principle cannot stop the collapse.