This situation is very simple. If your realtor cannot help you with this, I suggest that you work with someone else in the future.
I would also double check the seller's disclosures to see if they disclosed the pitbull next door.
Best of luck. Comsult with your agent. If not, perhaps a real estate attorney!
Incidentally, often it's not so much about the pit bulls themselves but the types of owners they have. Some are fine; some aren't. Evaluate the community.
Hope that helps.
Unless you and the seller modified it, your inspection period is the first 17 days from acceptance of your offer. If you are within that period of time, simply instruct your agent to cancel the escrow and ask for a return of your deposit. If you are past that time and/or have signed off on all contingencies, you may very well lose your good faith deposit. In that event, I would suggest contacting an attorney for further advice.
Good luck to you!
I suppose one could argue that a neighbor with a pit bull is a material fact that should have been disclosed, particularly if you have children, but you'd need an attorney's opinion on whether that would stand up or not. You might try having your agent tell the listing agent you're going to back out and why and see where that leads before taking any steps that might cost you more money.