This was an interesting read, and Habermas' approach is very different from previous philosophical traditions I've explored. The afterword — which responded to the objections raised by, among others, Nagel and Dworkin — boiled down some of the more technical arguments into more succinct, common-place language, not so dependent on the specifics of German state law, nor the framing of embryos as human lives which cannot be disposed of.
Habermas' primary argument is that human beings are defined by the nature of their existence as authors of their own life histories. Though parents can try to alter this history by education, training, and socialization, they can only do this as part of a communicative two-way process, which means that the child has some freedom to object to the aims of their parents, or to wholly reject them. Genetic modification is not like this, because the changes are not communicative —that is, the child cannot revise or reject the changes, because they are permanently written into their DNA. This is important because it irrevocably changes their identity formation, and threatens their claim to be equal with other citizens of liberal democratic societies.
As I see it, the difficulty of responding to Habermas' argument is that it is so rooted in this perception of what human life is like; he makes frequent recourse to German basic law as outlining intuitions that we would all share, and it is not clear to me that we do in fact share these intuitions. If anything, these claims increased my sense that there were legitimate grounds for disagreement before he even launched the argument about the authorship of life histories. Ultimately, I was not persuaded that these arguments stand up without assuming Habermas' wider social view; and I am not certain how easy it would be to detach the arguments about life history from these views. This notwithstanding, I found this a challenging and engaging position, and one that I will likely return to consider in the future.