A wormhole would normally collapse not because it violates any laws of physics but because it must obey them - in particular Einstein's General Theory of Relativity. Einstein (and Rosen) worked this out in the early 20th century while investigating the "Einstein-Rose bridge" that we would now call a wormhole.
Einstein couldn't keep a wormhole open because all the matter and energy he knew of was positive, and so according to his theory could only work one way.
Exotic matter is matter that is different in this key respect: it violates certain so-called "energy conditions" in general relativity that matter generally shouldn't.
In particular, it must appear for at least some observers to have negative energy. This is how it stops a wormhole from collapsing: whereas ordinary matter attracts, exotic matter repels, or more accurately in general relativity it causes spacetime to curve "in the opposite way" and so opposes the natural tendency of a wormhole throat to pull in on itself according to the equations of general relativity.
Now, whilst no one has ever seen exotic matter, and there is some doubt that exotic matter could really be created in any significant quantity - let alone manipulated and organised to hold open a wormhole - it as least theoretically possible thanks to quantum mechanics.
The attraction between two plates known as the Casimir effect is due to the negative (relative to the average) energy density between the plates.
So, since it is not actually impossible, it is possible and so physicists are happy to toy with the implications.
Even if that means also having to worry about time machines made from wormholes... but that's another story.
