There really is a lot going on, you're overwhelmed and your therapist understands, I'm sure. I think your anger is part of your therapeutic process and it's okay to feel and express it. Your therapist asking for permission to do this is a good sign - it means he's willing to take it slower if you're not ready or have a different approach if you need to.

The way he wants to work in no way whatsoever implies that you are not whole. In fact, working with the different parts was originally a technique in gestalt therapy, which promotes the idea of the person as a whole. The point of these parts is that we all have different aspects to ourselves and they don't always go together well. Such as having both positive and negative feelings about something. They're both aspects of reality but we need to work to accept that they're both true. But the very theory takes into account the person as a whole. Now I'm not sure if this is any relief to you, just thought I'd mention it in case it helps.

You are very intuitive and entirely right that these things have been protecting you for a very, very long time. Therapy comes in when they're beginning to become more of a blockage than a help. I know how hard it is and these things may even seem like they're no different from your self, it can feel dangerous. If you're not ready, you could just tell your therapist that. Or you could work out together a way to do it gradually or in some way that won't feel as threatening.

In my case, when something felt threatening to me in my therapy (for different reasons), I told my therapist about my fears, talked about the process more than the content to start with, and worked with a lot of art-therapy techniques. There are many alternatives, depending on your therapist's style too. Good luck!