Even though this book is directed at leftists (whoever they may be), the material covered would be useful for everybody. I think the book could be improved by devoting a chapter to in-depth analysis of a longer argument.
I have done university level courses in logic (through Cousera and EDX), and I agree with Prof. Burgis that the examples given are artificial and not applicable to the real world. Prof Burgis applies his analysis to real-world examples.
The material is presented in an accessible format. And the snippets of arguments given were analysed in detail. This certainly aided my comprehension of the material.
The part on symbolic logic would probably lose most of the general readership. Even though I knew where the author was going from my previous courses, he lost me at times.
My reason for suggesting a separate chapter on analysing a longer argument is that most real world ones encompass several methods and strategies. It would be good to see how these different approaches can be woven into a coherent whole.