Top set facing a made turn hand...deep stacks...tough spot

[BadBenOni]

I think you have some fold equity if you push,
he may have a low flush.

But the standard play is to fold, the maths says if he has a flush you dont have the odds.

I think a push is reasonable if you think he is loose,
he could have called with a straight draw on the flop and decided to bluff after you checked.
Or he could have a lower set.

This is poker, he could be lying.