why does the wage gap not exist?

Because of the law.

Men and women get paid equally, controlling for all other factors. The "wage gap" that many push simply does not take into account many other things, such as job, position, years of experience, salary negotiations, and timed worked. Controlling for all of these things, and you'll have about equal pay for both.

What does exist is an earnings gap, meaning that men and women earn different amounts. But, that's solely a factor up to the individual to control (by choosing different jobs, taking more time off work, etc.), and not society as a wage gap would be.

Because you said so.

federal and state law.

???