I live in the State of Delaware and I was charged with theft. I have a felony on my background and am currently going to school. I want to becomea behavioral health counselor. Although, I have had many people tell me that with my felony I won't be able to is that true?

The only way to be positive is to ask the licensing board. Some States/boards will NOT give a definitive answer until the application is formally made but they can give you an idea of what the outcome will be.

Can no one at school tell you?

Well, most employers will do a background check and depending on the outcome whether they hire you or not. Also, as Judy says, if you want to get licensed you will have to have a background check done there too. From my experience, they do not discount you just because you have had a charge, but you may want to find out how they determine eligibility.
I think it would be the same with any profession and doing a background check. There are pros and cons to the field... in some ways they are very understanding of past experiences and sometimes it is just a legal matter that they have to follow.
Good luck. I would do more research.