Yes, there’s a double standard. It exists because women have a lot more to lose by being promiscuous than men do. Men generally do not cotton to the idea of raising another man’s children, and unmarried women who begat children often found themselves — and their offspring — at the mercy of the elements.
Men who were wealthy or powerful could afford to pay for their bastard offspring, and could use extramarital affairs as a way of propagating the bloodline, if not the family name.
Double standard? Yeah. But biologically inspired and sound.
And of course the guy has no responsibilities. Right.