I think it's more that fathers / mothers want to protect their daughters from the wrong kind of guy, rather than objecting to the idea in itself. There are a lot of jerks out there, I'm sure no one will be suprised to hear. Teenage brains are not exactly the most discerning decision makers either, so a parent could understandably be concerned about his / her daughter's hormones making the decisions for her, and her falling for a boy who ends up being a mistake and an eternal regret. Then again, perhaps that boy will grow out of his youthful.... youth and end up being an equal member of the relationship.
And what about the converse? How do mothers feel about their son meeting and interacting with women?