They conceive themselves as private citizens with singular opinions striving to be heard within a cacophony of competing voices and opinions. They don't decide what we see, in other words. They only argue about whether it is worth seeing or not. Curators, however, do decide. They include and exclude, and, as a consequence, the eccentric, combative tastes and opinions that constitute an art critic's abiding virtue, quickly become vices in curatorial practice.
Critics have freedoms commensurate with their lack of power.
Curators have responsibilities that derive from their actual power to exclude, so they must always see themselves, in some sense, as public servants. When two curators agree, their agreement is taken to represent a consensus of public taste. When two critics agree, one of them is redundant. Thus, in much the same way that artists curated into exhibitions by theorists risk being seen as instruments of that theory, artists curated into exhibitions by critics risk too close an association with the eccentric visual agendas that are a critic's stock in trade. Also, since a critic without enemies is not really a critic, critics who mount exhibitions are, in effect, sharing their enemies with their friends.