How could it NOT be cheating? Because it’s not with women? Because it’s “just” sex? Did you commit to “forsake all others” is your marriage vows? What is sacred about marriage if not being faithful to each other?
He’s using a tactic called “gaslighting” on you. Look it up. It’s where they try to psychologically confuse you in order to keep you off balance. He may even believe his lies. But you don’t need his permission to hold your own views.
Was / is he hiding his activity from you? If so, that’s proof right there that he knows it was wrong and shameful. You caught him, so he only has a few options. 1) Lie about what you’ve found, 2) tell you he won’t do it anymore, or 3) tell you that what he’s doing is permissible. #3 allows him to continue the activity. And if you’re still intimate with him, endangers your health and even your life.
You have every right to tell him that it is cheating to you, no matter what he thinks. And that you demand that he stop in order to remain married to you. But be prepared for him to agree, but then continue his activity with more vigilance toward secrecy.
The fact that he’s able to twist your thinking means he’s likely been doing that for years.
It’s cheating, any way you slice it.