The phrase "cheap act of self promotion" might be viewed as offending, and is surely unprofessional (it's just the reviewer's opinion). I'm a hothead, so I would point this out to the editor and ask him to discipline the reviewer.
Overall, self-citations are a way of self promotion – yes, you point the reader to your earlier relevant works in the topic, but you also advertise your previous papers in hope that those that missed them will cite them in their own future articles. Citations are a valuable asset in academia, so it's not surprising authors go after them. Self-citations, however, don't stand on equal grounds as citations – in my field, many evaluations require "number of citations excluding self-citations", so self-citations are not just an easy way to boost ones metrics.
Referring to one's earlier works in the topic is definitely a good thing, showing the author's experience, linking to previous state-of-the-art, and simply telling a story that's behind research ("previously, I've made the analysis in 1D, and herein, for the first time, a 2D analysis is performed"). If your self-citations fulfill any of these roles, I see no reason to remove them.
In the response to the reviewer point out the relevancy of the citations used, like Solar Mike suggests. And the 6/44 ratio is all fine to me – after all, you're the expert in the field, so it's natural you have achievements. If it was 38/44, that would look silly.
Heck, I've seen reviewers flooding their (anonymous) reviews with a list of "suggested" references, orbiting around one author – it's hard not to be convinced about the identity of the reviewer, and think of it as a "cheap act of self promotion"...