First, it is important to give some context to the allowance in the Orthodox Church for remarriage. Subsequent marriages are always considered "penitential"; only the first marriage is considered to have the high esteem that the Wikipedia article mentions. In terms that the Latin Rite of the Catholic Church would use, only the first marriage is sacramental. Theologically speaking, the Orthodox Church doesn't approve of subsequent marriages, but merely tolerates them, as a concession to our fallen and broken human nature.
Why does the Orthodox Church tolerate subsequent marriages? It is hard to escape the conclusion that this practice was foisted upon them by the Byzantine Empire's law, and simply continued to exist to the present day because of historical practice.
But the question doesn't ask about remarriage. Instead, it asks about divorce. I think it can be argued that generally the reason why divorce is sought most of the time is precisely so that one of the parties may remarry, and thus my answer above stands: divorce that was a precursor to remarriage was foisted upon the Orthodox Church by an Emperor who wanted to divorce his first wife, and then simply expanded from there.
However, it must be admitted that even the Catholic Church allows divorce in some extreme cases. One such instance might be if there is significant physical abuse between the spouses and/or their children --- and divorce is the only way to protect innocent lives (or their physical health). Christian charity demands that in such extreme cases one does what is possible for the protection of innocents. In such cases, all Christians (including the Orthodox Christians) would have allowances for separation, and even civil divorce if that is the only way to secure important legal rights --- such as child support, etc. But in the eyes of both the Catholic and Orthodox Churches the civil divorce has no effect in the "mystical" marriage itself. Where the Catholic Church parts ways with the Orthodox Church is in the latter's allowing of remarriage.
So, a partial answer as to why the Orthodox allow divorce: as a precursor to remarriage --- which they have historically allowed, even if grudgingly; as necessary for self-protection --- just like the Catholic Church --- for sure; and what else? I am sure they would have jurisprudence on what other circumstances would count as serious enough to break the visible union of husband and wife (even if not the sacramental marriage bond between them).