The problem here isn't with you, it's with your boyfriend. He can't tolerate his own weakness, feelings of vulnerability, helplessness, impotence and dependency needs. So, whenever you feel weak, you naturally pluck those notes inside his soul.
He can't tolerate those feelings in himself, so he tries to squash your feelings. If he can extinguish your feelings of weakness, then he can make his own anxiety die down. Know that this isn't your problem. It's his.
Each time you allow him to point the finger at you, you are allowing him to focus away from himself and onto you. That's exactly what he wants you to do. Not only doesn't want to own his feelings of weakness, he doesn't want to own that he may have an issue here.
If you allow him to point the finger at you, and your 'problem' you are taking the bait and allowing him to divorce himself from his own issue.
So, know that you are entitled to your feelings of weakness. Know that you are actually strong, stronger than he is. You are willing to tolerate feelings of weakness, which takes great strength. Don't let him or anyone else tell you that you aren't allowed to have your feelings.
Next, you have to decide what you want to do with the information I'm giving you. One thing you might do is gently put the issue back on him. Each time he tries to place the focus on you and what's wrong with you, simply say, 'You don't like to feel weak do you?' Or 'What's your objection to feeling weak?'
When he tries to turn the conversation back to you, just return to him again. You might also tell him, 'Part of being a human being is allowing oneself to tolerate all the emotions. And, feelings of weakness are part of the human condition. I know you don't like these feelings, but they are a part of life.' If you stick to your guns and don't let him pin this on you, little by little he will have to face his own music.