While the grammaticalization of person agreement is a widely-cited and apparently uncontroversial topos of grammaticalization theory, the striking differences in the outcome of subject pronoun, and object pronoun grammaticalization, remain unexplained, and the relevant literature continues to assume a unified grammaticalization pathway. This paper argues that the grammaticalization of object pronouns is fundamentally different to that of subject pronouns. More specifically, although object pronouns may be rapid early grammaticalizers, often losing prosodic independence and cliticizing to a verbal head, they do not advance further to reach the stage of obligatory agreement markers typical of subject agreement. Typically, object markers remain at the stage of Differential Object Indexing, where their realization is conditioned by a bundle of semantic and pragmatic factors exhibiting close parallels to those operative in Differential Object Marking. Evidence from language typology, and from the diachrony of person markers across two millennia of Iranian languages, is adduced to back up these claims. Thus the widely-assumed grammaticalization cline for the grammaticalization of agreement needs to be reconsidered; for object agreement, there is evidently an attractor state, that of Differential Object Indexing, beyond which object agreement seldom proceeds. Finally, explanations grounded in discourse data are proposed, which also account for why obligatory object agreement in the category of person is so rare, while gender and number agreement for objects is far less constrained.