Why don't cats eat snails?

Yes, there is something inherently repulsive in snails: their slime, which is sticky and sometimes stinks or tastes bad. Snails not only produce it to slither over surfaces, when they are attacked or injured, they produce lots of it as a defensive mechanism, relying on the attacker being grossed out by the sticky slime in their mouth. Most animals find it repulsing, not only cats.

This article states:

Land snail defenses against predators include cryptic coloration and texture; thickened shells and aperture barriers; defense mucus production including irritating smells and tastes; hiding behaviors, and rapid withdrawal or dislodging movements

Another reason is that cats evolved to eat small mammals, like rodents, and birds. Those have a very specific mixture of protein, fat, minerals (like calcium) and fiber in their bodies that the cat relies on for nutrition. Snails, on the other hand, don't contain as much protein, very little fiber and almost no fat at all, as pointed out in this paper about feeding snails to livestock:

In general, only a portion of the normal diet should be replaced by snail meal because of the possible lower protein content and poorer amino acid profile compared to the normal high quality fish meal diet.

product	country	protein	fibre	fat	ash	calcium	phosphorus
Snail meat, fresh	Philippines	53.3*	2.5*	1.1*	26.6*	7.2*	0.59*

'* All values indicate the percentage by weight of dry matter, which means the numbers are even worse for fresh (slimy) snail meat.

And lastly cats are lie-in-wait hunters whose prey drive is stimulated by movements and shuffling sounds, instead of foragers who would pick up a snail as an easy snack.

As pointed out in several comments, this does not mean that cats never eat snails. That your particular cat doesn't like snails can be personal preference - or rather aversion.