Absolutely with Bill here. Do not engage in this conversation. Your giving him room to excuse his behaviour.

He doesn't have a right to ask you why your online, when your online.
My partner and I don't live together. Sometimes I am online when he is and I don't contact him and vice versa. Wouldn't dream of expecting an explanation for something like that.
Your leaving the door open by not letting him know you don't feel it's working.
He isn't psychic, he will keep asking until you explain.
So just let him know this isn't what you want.
Thanks but no thanks.
Then block him.
You know this guy is a liar, so there is no reason to give him more chances to keep lying.

Why are you so afraid to let him go?
We don't fall for abusers because they are a**holes all the time. Usually the contrary, usually they are complimentary, attentive good at building you up as a unit/couple. (We don't need 'them' (family/friends), it's us against the world baby. Etc,etc)
They make us feel good.
Then when they tear us down, we think it must be us because look at everything they have said and done.

Thing is is the good with these people is always really good, but the bad....it isn't worth it.

I don't have close family and only a handful of friends. And I wonder if now would be the time to try focus on rebuilding friendships, and taking a break from relationships until yo have conquered this negative cycle.

Best of luck.💙