In a pleading there is normally a fact section, a law section, and a section that applies law to fact.
In an answer, if your jurisdiction has a general denial you can deny generally. If not you have to go point by point and say either admitted or denied.
Somewhere in there is a section that talks about the cause of action (or the claim) he is making against you. There is more to it than I paid this or that. Somewhere he has to be saying we were both jointly obligated on the mortgage, I paid my part, she didn't pay hers, that sort of thing.
Still your lawyer can write a letter and explain the omissions. She couldn't pay her portion because she was forced to move out by his constructive eviction. She had to locate housing elsewhere at a cost of $________. She had to pay movers at a cost of $_____________. At the time of the purchase the parties committed to one another to be in an exclusive relationship and to live together and share the benefits and burdens of the contractual relationship. He unilaterally chose to leave the relationship. But for his actions in leaving the relationship and constructively evicting her by creating a hostile environment, she would not have had to move and locate suitable housing elsewhere. Etc. I think you get my point.
There are ways to deny the basis for a claim without pursuing a counterclaim. These include various defenses. Some examples include:
