He admitted the affair.
I wonder why he did this, preparation of leaving you.
Seeing if you are willing to fight for him, ego trip, make you jealous.
Ow about to spill beans and got in there before her.
Wants to use this affair as a means to get you to pull your socks up and give him more attention.
Wants you to end the relationship and set the ball rolling placing blame on you for ending marriage.
Setting you up to accept fear of losing him and enabling him to have cake and eat it scenario.
Who knows, probably best asking his affair partner, doesn't sound like you will get the truth from him.
Regardless, what do you want, curently you are confused as to why he is changing his mind leaving you with little thoughts of what your boundaries are in this situation.
Have athink about what you are prepared to put up with.
Proceed to protect your finances.
Appointment with solicitor.