Leonato was so cruel to his daughter, because she has been classified by Claudio as anyone but an innocent maiden, meaning she has lost her virginity before the wedding to another man. This was considered to be very sinful, and like StephanieRR stated, it was indeed like a death sentence for them if their father found out. The actual irony was that Leonato remained very calm for what he found out. I'd assume most fathers 'back then' would have been much more brutal.
Hero is a victim of social stigma. Leonato loves his daughter and cares above all else for her well-being. Unfortunately, during the time of this play, the most important and protected part of a woman was her honor, a.k.a. her virginity. Leonato went to the church with the expectation that he would see his maiden, pure daughter married off to Claudio. When he hears accusations from two trusted men, Leonato believes them over his daughter and thinks Hero had sex with some random guy without her father's consent and outside of the marriage bed. This was basically a death sentence for the woman back then. She was "damaged goods," and those don't sell on the market. Leonato was truly in anguish over the fact that his precious daughter was doomed to a life of a dishonored lady. In his anguish, he curses Hero and calls down shame upon her, because of course it was always seen as the woman's fault in these cases. He says it would be better for her to be dead, or never born at all, rather than fall into such disgrace.
In short, Leonato was cruel to his daughter because he was raised to be so in these circumstances.