Husband wants divorce but won't file. ?

Because he is hoping the treat of divorce is enough to get you to toe the line OR he thinks now that he has mentioned divorce, he is "separated" and can go off acting single without having to actually deal with the paperwork? 

He is hoping things can change. Can they?  Can you both sit down and work out the problem? No yelling, actual talk and actually trying to fix the problem.

I am sure you would love to hear that it is because they have second thoughts and wish to reconnect, but the reality is that it is most often because of their laziness or not wanting to incur the expense of a lawyer and court costs.  Often separation solves the immediate problems, thus without pending issues (like another relationship), there is not enough reason to move forward.

holly:   You will have more control of the matter if YOU file.   Get a good divorce lawyer - ask family, friends, coworkers, etc. for recommendations.   

Good luck to you.   

He's being a turd, get your proof that he wants a divorce, like texts or emails, then you file.