So watsonianly, a number of reasons.
1) institutional inertia, of an institution that has lasted centuries. This exaggerates the effects of other problems
2) Watchers wanting control over Slayers, and want an advantage if they need to face them
3) They historically haven't been useful.
-a) First, they just don't do much to vampires and many demons, hence the use of crossbows
-b) Up until the repeating pistol, they weren't all that practical in a fast-paced close quarters urban environment
3) A slayer with a gun isn't significantly better than a normal with a gun, so there is comparative advantage to solving gun-solvable problems yourself, and have the slayer take care of the harder stuff.
4) Don't give vamps good ideas
5) Do slayer skills at weapons even apply to guns?
So, hopefully on a lighter note:
1. Definite institutional inertia, the Watcher's Council was definitely a "tied to the horse and buggy" kind of group...which makes you wonder how the hell they lasted this long. But hey, Whedon-logic.
2. That would make sense, again, Evil Patriarchy (TM).
3. Well, firearms has been an evolutionary process. Indeed, until repeating firearms came into existence they weren't all that useful for CQB. But even then, once firearms technology began to mature, rushing to go hand-to-hand was slowly starting to go the way of the dodo just like horse cavalry. But now with modern automatic weapons? Ignore them in CQB scenarios at your peril. The Watcher's Council apparently does, but again this probably ties into the previous point about them. And they can be useful against certain types of creatures, vampires included, depending if they are sensitive or vulnerable to certain materials that can be packed into ammunition, whether that be garlic essence, silver, mercury, wood shavings, etc. And yes, I know making silver ammunition is a LOT harder than it actually sounds, but it is possible. Then of course, there's incendiary ammunition, explosive, etc. depending on what caliber/mm you're using, or shotshell.
4. Firearms are tools. They don't necessarily make the Slayer better, but it is an additional useful card in the deck she can use to her benefit. Plus....MORE DAKKA.
5. But you WANT to give vampires good ideas, if not horrific ideas, admit it.
But it's inevitable....sooner or later, one of the undead will have a lightbulb go off in his/her head.
6. Do Slayer's skills apply to firearms? Well....that IS something to ponder and discuss, isn't it?