I don't know if it is about blame. But it is what it is. If a person is inclined to become overly dependent on others (T's or otherwise), that is probably not just a therapy issue, but an issue throughout their life -- perhaps due to lack of confidence, poor self-esteem, anxiety, etc. One of the goals my therapist worked on with me a great deal was to help me find and exercise my own independence, to find my own sense of autonomy, so I wasn't so reliant on what everyone around me was thinking, so that I didn't base all of my choices on what I felt obligated to do for others for their approval, etc.

I've never had a therapist encourage unhealthy dependency. Rather, I've had them encourage me to not feel guilty about asking for help when I needed it, but they at the same time, encouraged me to find the balance of independence and healthy acceptance of support. I think it can be easy to slip into a sort of helplessness in areas of life where we can probably function much more decisively and independently, particularly when we are dealing with depression and anxiety which can make us feel rather paralyzed. It is much less about blame and much more about change of habit of thinking.

I don't know what your T meant by letting go of dependency unless, like I said above, your therapist is seeing a tendency on your part to not trust or have confidence in your own ability to work through certain things. Without context, it is hard to say.