As for the example of "congressman" (which seems pretty inelegant as-is), I suppose the distinction is made in terms of concurrent number. I mean, there would be only be the Chairman of X at a given time but there are hundreds of members of Congress at any given time. While it might be technically correct, if we are to consider "-man" gender-neutral (but always, also?), to refer to a mixed group of members of Congress of as "these fine Congressmen", it seems strange.
Of course, this could be avoided simply by calling them "Representatives", but it raises an interesting question. Is it appropriate, for example, to have a "Conference of Chairmen of Foreign Affairs Committees of Parliaments of the European Union". Or should it be a conference of Chairpeople, even if it is correct to call a woman "chairman".
I believe the preferred usage is "congresscritter".