i agree with KaylasMom,
Not telling them the breed isnt lying, its just being safe.
It seems like alot of the time the trigger word for people is pitbull, and if they watch alot of news then im sure they would picture an agressive, huge, uncontrollable dog which 95% of the time isnt true.
There are some great organizations that can help you find an awesome home for your pit, like HugABull or if your in the states then Love-A-Bull is a good one to.
Im currently looking for an apartment for the summer when i move and i was really surprised at how many of them allow dogs as long as you put a deposit down.
So dont think the only option is to give your pit away, there are many other things you can do to keep your dog.