You have to know that there were a lot of people--myself included--who were willing to give you a chance as Chancellor. You failing at being Chancellor would no doubt damage schools and kids, something none of us wants. As much as we were skeptical of a total outsider coming in and running the schools, a lot of us hoped (perhaps against hope) that you would nevertheless have a successful and productive run at the job, for the good of everyone involved.
But you don't seem to understand that you are now a public servant, just like everyone you now supervise at the DOE. You are not accountable to stockholders, but to stakeholders, for whom the issues to which you were (maybe?) listening at the PEP meeting on Tuesday night are matters of, if not quite life and death, certainly life itself. Your sarcastic response to a crowd, even one which, I'll grant, was pretty unruly at that point, was not becoming of a professional of your stature. Teachers are frequently warned against deploying biting, negative sarcasm with students; the fact that you don't seem to know this gives your detractors more fuel for their fire of criticism.
Most of the commenters at the City Room blog linked above were pretty harsh, though certainly civil and fair. They characterized the response as unprofessional, inconsiderate, and displaying a certain lack of consideration for the common woman and man. I have to say I agree. I've been unpleasantly surprised, Ms. Black, by how unprepared you seem for this position in every aspect. One could forgive, maybe, a certain lack of finesse with the minutiae of DOE policy and educational thought were it handled openly and honestly and with a strong dose of modesty and consideration. We're not seeing that. Mostly I'm just struck by how the basics of Teaching 101--civility and respect towards the students, patience, humility, a willingness to learn from those gone before, the courage to listen as well as speak--seem to be lost on you. It's hardly shocking, then, that 80,000 teachers wonder how they can respect you as their ultimate supervisor.
So where to from now? It would be flip of me to say that you should continue to let Deputy Mayor Walcott and Deputy Chancellor Polakow-Suransky do most of the talking for you. Maybe for the next week or so, at least. But long-term, you need to come to terms with who you're serving, ultimately--children and their families, not Mayor Bloomberg--and decide if you're the right person to carry out that role.