Is it fair for my boyfriend to accuse me of cheating?

During me and Jake, my boyfriend, "break" I had another boyfriend during those months. I say it in quotes because me and Jake were not official and we parted without a clear explanation. This was also very frequent where we had long breaks with 0 communication.

Jake became obsessed with my "affair". He calls it cheating. He said we were still together during those periods even though we have constantly parted and reunited without reason.

We've had an on and off relationship and he has never publicly recognized me as his girlfriend before. This only changed after I told Jake about my other boyfriend. I told Jake how my other boyfriend appreciated like he never has before. I did it with intention for him to step up and be a better partner.

He says that I'm not acknowledging what I did was wrong, therefore, I'm bound to repeat it if we ever separate for a period, such as school, work, family.

Even though we were never clear about the relationship we had prior to my "affair", he claims I was cheating. He always brings this up as cheating. He is also very paranoid that I am cheating.

Is it fair for him to make this claim of me cheating ?

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