‘But he who stands steadfast in his heart, having no necessity, but has power as touching his own will, and has determined thus in his own heart, to keep his own virgin state, shall do well.'
We must interpret this verse in the light of 1 Corinthians 7:36. It cannot therefore be saying that if the man nobly determines to force his daughter to remain a virgin against her will he is doing well. That would be heartless and wrong. It must therefore be referring to a man making a decision about himself and we must add ‘state' to virgin as we have done in the translation. This would then favour 1 Corinthians 7:37 as referring to father and daughter.
Here then Paul is commending the man who is able to have full control over his own will, and is confident of his own steadfastness (and he should not be if he has strong sexual desires, for they will eventually wear him down), and is full of determination to lead a single dedicated life. That man, he says, does well.
Alternatively Paul may be signifying a case where father and daughter are equally determined, and the father may in some cases be hesitant, either because he wants grandchildren and male heirs or for the sake of status. In these circumstances he would not be behaving ignobly towards his daughter (1 Corinthians 7:36). In this case, Paul says, by denying himself for the sake of his daughter's desire and dedication he does well. This would fit in better with 1 Corinthians 7:38.