The problem is trust. Intentionally insulting someone by means of pronouns is bad. Few people disagree with that, and it has been forbidden by the original CoC from the beginning.
If people assumed that that's all the CoC is about, there wouldn't be a problem. The problem is that users assume bad faith on the part of those who enforce the CoC, and are afraid the CoC will be abused as an excuse by SE staff to ban them at will, with no realistic chance of appeal, and smear to their reputation on top.
They believe this might happen to them because they believe the same thing recently happened to a very reputable, level headed, and respected member of the community. In the absence of trust, users are looking for a bulletproof CoC that cannot be abused against them.
Stack Exchange has gone to great lengths to reinforce both of the aforementioned beliefs, to a point that some feel can no longer be adequately explained with incompetence.
