The trouble I had was with dissociating my thinking mind, or Tolle's ego, with that of the observer mind; in reality, and materially, they are one and the same. As I remember, he draws a sharp demarcation between the two types of mind, labeling the egoic mind as a sort of curse on humanity.
To me, his egoic mind parses as the rational mind, or the thinking mind. Therefore, his dismissal of this aspect of our consciousness leaves much to be desired in my case.
I mean how am I supposed to read and understand his book, written in English, without the aid of a rational mind?
Perhaps it's because I didn't make it past the first few pages that I didn't understand his message, but I found Chopra much more accessible in this regard.
As to your question here: "Who is this "my" who has a goal in meditation"
The my is me; all of me. Not just the observing me, not just the thinking me, or the feeling me, but the inseparable combination of the three.