I finally pulled the plug on my 2.5 yr relationship. I held onto hope that we could improve our communication and our love for one another would prevail. I felt calm straight after the breakup, sad but OK, now 3 weeks later I feel in bits !

I am really struggling to let go. My heart wants to hang on so much. The good memories and the fun we had, the shared interests.
I miss our routine, I miss our conversations. I miss our times together.
I don't miss his critism when I didn't cook the way he wanted, when I didn't parent my children the way he thought best. I don't miss his lack of empathy for those in difficult situations or those for whom life has been tough.
I feel panicked and want him back, why is it so hard to let go, I thought the hurt I have felt before would get me through our breakup

NO ONE is the 'real' one at first, for the simple reason that you don't know them enough.
When you do know someone, the good times are a memory of something that can never be again, because it wasn't real. It's like wishing you were a virgin again, innocent of anything to do with sex. You can't go back. The memory is of something that DOESN'T EXIST. When you can accept that, the faults he has will be more prominent in your mind, and you will realize you did the right thing.
Plus, he sounds selfish and childish if he claims you drove him onto a dating site the day you broke up with him. On the other hand, what he did the day you broke up is no longer any of your business. You two weren't properly 'done' with each other, and you need to make a 100% clean break, with no contact.

It may not be apparent at this moment, but if you move forward and continue on with your life you will be happy again. There are plenty of other guys out there for you, even one that you can share such intensity with all the time you're together.

For now focus on the present and plan for the future, don't get hung up on the past.

An ex is an ex for a reason there may have been good memories but what percentage of the relationship was like this? Obviously not enough to let go, you deserve to be with somebody where love, laughter and communication comes naturally and in time you'll realise this :)