The problem with these verses is that they are somewhat exposed to two interpretations in the Greek. In the Greek is more like this:
If anyone thinks he is behaving unseemly to ‘the virgin’ (either daughter or spouse) and if to be ‘beyond prime’ and so it ought to be what he wants. (my paraphrase from the Greek English interlinear Bible)
The key points of split between the two interpretations are whether the virgin is a daughter or a virgin that a man wants to marry. In the case of it being a daughter, ‘beyond prime’ means she is at the ‘matured point’ of being a spinster. If she does not marry soon she will be disadvantaged, this is why the Father wants to give here away and is wondering what God’s will is. There is no reason why He would not also be consulting her daughter on what she wanted as well. If on the other hand we are referring to a man who is wondering if he should marry a virgin then ‘beyond prime’ means beyond his self control in terms of lust. He really wants to marry not because he is worried about the woman becoming a spinster, but because he wants to have sex with someone really badly.
I think in the context it seems more honest to the text to take the first option. We are talking about a Father’s questions about what he should do. There seems to be a sense that the virgin somebodies possession, either a betrothed or a father. However from what I understand of engagement in Hebrew society it was as good as marriage itself, so I do not think it would be moral to back out of it after you have already been engaged unless there is good cause. This is more about if a Father should give his daughter to a man, to be engaged to her.