You've only been with her for 3 months, right? Unless you've already pledged your eternal soul to her, are already engaged or contemplating marriage in ANY way, reconcile yourself to the simple fact that LOTS of relationships do not work out, for no fault other than differences in ideals.
Though this may seem to be "the one thing" that is so bad in your relationship as to cause it to break, this is an issue of trust. All notions of upbringing aside (and this has been said by several, i'll say it again), this is simply about trust. If her trust in you is so easily lost- not even weakened, but destroyed by a totally unquestionable ultimatum- then you have very little or no chance of it surviving in the future.
It's not that big a deal. You don't have a house together, marriage, 3 kids and a dog named Shep- you have a 3-month girlfriend. Let her go, rip the band-aid off (be blunt, don't let her try and stop you, walk away clean), and it rest. I've tried to let girls go easily, it doesn't really work. You only, in the long run, cause them more pain. 3 or 4 months is nothing... wait until you get the one that sets you floating. If this girl doesn't already make you float, she should even be in the running.