Why do they go to all the trouble?
Why all the game playing?
Maybe the game playing is what they want???
He was so keen, he looked after me for a week when I was ill, he told me he had really fallen for me, he told his family ie brothers and sisters about me and how happy he was, he asked me if I was keen on him because if I didn't want a relationship he didn't want to tell his (adult) children, but he told them. We both came off dating site together, his suggestion not mine but I was happy to do it. He met my (adult) children. He talked about things we could do in the future, places to go
Longhairedcat, I think that is very full on for something that had only been up and running for two months.
You like everything out there where you can see it (maybe this is why the full on nature of it doesn't strike you as odd?) and he is being all mysterious. This isn't going to change. You are going to keep on ferreting away to get to what is real about him and he is going to keep on hiding and refusing to communicate. Basically he is dangling enough of himself in front of you (literally...) to keep you interested and in order to know he has your full attention. But when you try to get close or get to the truth he walks away and lashes out at you into the bargain. He wants you to try to correct the mistakes he made about you (blaming, etc) and he will make accusations again in order to reel you in again next time something comes up. He also wants you to apologise and ask him to come back. This is game playing and the opposite of a match made in heaven.
Watch out for the tendency to want him to chase you. It will hurt if he doesn't, but suck it up. And do not fall for it if he does. I think he is quite a shallow person by the sound of things and he would only chase you to salvage his own pride and not because he likes you.
Also, watch out for very early declarations of falling for you, being in love, etc. such as happened here. Ask yourself why these statements had such a strong effect on you.