exclusive friendships

Boyfriend had a friend when I met him. A single female friend. Used meet her for drinks, have chats on phone, text each other... All innocent. On both sides. I suggested a few times I join them. Fell on deaf ears but wasn't struck off the list. So carried on. No drama. 
As time went on tho, and I was a. never invited and b. my suggestions of joining them were rejected, I became insecure about the friendship. The more I suggested I meet them, the more excuses came my way. All valid but never quite enough. 
I met her by chance in the hairdressers. We chatted, and as far as I was concerned, it was a nice chat. She reported back to him saying I asked too many questions, as if I was fishing for info. I wasn't. Ffs. She'd been on hols and I was asking how they went.
So now she doesn't like me. Ok. But weird. I asked one final time earlier in the year if next time they meet I could meet too. Boyf said ok. Next time they meet I'm out of the country... Coincidence? 
I know nothing sexual going on, but why the need to keep us at arms length? 
He went out with her for burger and beers one time. I was home when he was getting ready. And he put on his best jeans, nice shoes, did his hair, was dancing around all excited to be meeting his friend. He got home two hours after the pub closed. I know 100% nothing sexual is going on. But I was still upset. Especially when the following week at my bday he was going to meet me after work, not dress up, and assured me we would come home early. Seemed she got the better night. 
Anyway, just felt like a big secret. And when he did this before it was because the friend was a ex and he didn't want me being friends with her cos he was afraid I'd find out and force him not to friends anymore. I found out about the lies, had a chat with her over a coffee, she said they've a special connection that I'd never have, and said lots of other things too, and yes, I forced him to dump her as a friend. He did. Eventually...
Anyway, back to the other friend. I've told him I don't want him not being friends with her and actively suggested he ask her advice on stuff. I just asked if I could be involved. If she doesn't like me, then why doesn't she give me a chance and she might like me after properly chatting to me. I suggested she come to ours for dinner. Anyway he said that would never happen. I asked him to see all this from my POV, asked him to put another of his female friends in her situation (as in, pretend this girl was Anna - one of his besties - yes he has other female friends that I'm completely comfortable with, he's even friends with some exes and I'm totally cool with it) and he got it. He ended up stopping that friendship. Much to my disappointment I might add. But he said he could see where I was coming from. 
I thought it was all sorted until we saw her in the park last weekend. Stopped. Chatted. Left. He gushed about her. And I got all insecure that he'd start that friendship again. Had / having massive argument. 
He says I'm controlling and being manipulative. Am I?