How can I clear myself of emotional attachment when reading reviewer feedback?
Personally, I find that the following process works well for me:


Complain together with my co-authors about the blindness and foolishness of reviewers, the sorry state of publishing, and the general existence of injustice in a world not ready for the pure angelic beauty of our work.  Remember not to take this too seriously.
Ignore everything for at least 24 hours, letting my initial emotional response settle and giving space for rationality to return.
Copy the review responses into a template for a response letter, separating each statement for its own response.  This effectively forms a checklist of work to be done (or at least to be clearly explained why it should not be done).  I do this even with conference papers where there is no response letter, because of the organizing benefit.
When revising, focus on only one statement at a time, taking it in isolation and working until the comment has been fully addressed and I can write a clear and non-emotional response explaining what has and hasn't been done and why.  Depending on the overall tone of the situation, sometimes I will start with the little things and work up to the bigger ones, and sometimes I will do in the opposite direction.


Finally, as I work, I always remind myself that every statement by every reviewer can teach me something that will improve my paper, even when I disagree with it.  Sometimes, the reviewer has valuable insight.  Other times, their apparently "crazy" or "ignorant" reactions are instead actually showing me how I have not spoken well to the community of readers, have opened myself up to misinterpretation, or have allowed my work to be viewed as part of an intellectual battle that I do not wish to participate in.

We are emotional beings, and we have emotions.  Over time, you will hopefully learn to read the curve of your emotional response so that you can ride with it and manage it rather than fighting it or amplifying it when that would be counterproductive.  The process that works best for you may vary, but one way or another I think that it is best to acknowledge emotions and then find a way to let them settle before trying to work with the criticism.