My last partner was 8 years younger than me and he pinched my birthday too that felt weird someone else getting greetings and cards on my day (I normally am a great sharer of anything but it did feel weird and I never quite got to feel comfortable inwardly) I was in my 50 s
The age difference was not a problem as I remember it , the relationship however was and after 8 years we split acrimoniously he very very quickly found a wife followed by a child
I think the bit to concern you is not the age difference but the fact that he doesn’t acknowledge you in public that would be a big warning sign for me Even if he’s a private man who doesn’t show affection in public you would expect him to be a bit more ‘together’ than you say however 2 months is a very short time and perhaps he’s a cautious man or maybe been hurt before and taking it slowly
Ask him
Morecambe and Wise - the lost tape


