It's a standard human defense mechanism: If someone gives me a hard time, I am apt to find fault in my critic, in return. Thus, per a talmudic observation which is echoed in general society, we have a hard time accepting rebuke; our own critics' flaws are so large and glaring that any rebuke is easily dismissed as coming from an unworthy source.
As a result, it is understandable that a Rabbi might respond to criticism by looking down on his critics. Indeed, one relative of a synagogue rabbi once warned me [before I entered the rabbinate anyway] that many synagogue board members were frustrated at their own lack of authority in their careers and at home, so that they joined the board to find someone to boss around, and upon whom to take out their frustrations.
This was a rational, if unproductive, response to criticism.
The reaction is not limited to Rabbis, of course; I've heard the same sentiment from community workers in other Jewish institutions, as well as in non-Jewish institutions. All of us receive criticism, but those who invest their greatest efforts in working for the community tend to receive it more than others, and may well grow frustrated and lash out in response.
Four observations, though:
1. In my experience, the idea that people join synagogue boards in order to lord over others is rarely true. Everyone has their faults, and some people use authority to validate themselves, but that's about where it ends.
2. This kind of perspective is damaging to the Rabbi. Putting down your persecutor doesn’t make you any better at your job, and is likely to make you worse at it.
3. A gemara in Nedarim (81a) asks why the children of Torah scholars do not become Torah scholars. One answer offered is that Torah scholars are guilty of calling regular people "donkeys"; apparently, this sort of disdain is a turn-off to their children, let alone others. [See Chatam Sofer there, who cites a related passage from a gemara in Shabbos which I cannot locate in our editions.]
4. Finally: Even in the case of a critic who is acting out due to personal weakness, the Rabbi might ask himself whether he has an opportunity, and even an obligation, to help this critic grow. As I've cited here before, Rav Chaim of Volozhin insisted that the sole purpose of our existence on Earth is to help others; if so, this critic may need help in realizing his Divine mission. If the Rabbi can get past the pain of his experience and find a way to help the critic become more positive and productive, he will have accomplished a great thing.