What you are describing seems more like a difference in the way you and your T are seeing yourself rather than about readiness or not in relation to therapy. I've been really frustrated in the past when I had a T telling me how well I was doing and how much progress I'd made etc. because it didn't match at all what my experience was. It felt dismissive when he intended it as encouragement; and also left me feeling helpless because he didn't understand the severity of the way I was viewing my life. I hope you can keep sharing with your therapist about the differences in your views; and also ... I like what Chris mentioned about being able to be:

maybe your T is focussing more on the strong independent side; and you are focusing on the very broken instead of you both seeing the fuller picture?