EPCs predict divorce rather than EPCs causing divorce.

from The Myth of Monogamy by David P. Barash page 102 nonfiction ~1 min read

Thus, divorce and EPCs could be intimately connected as part of a "mate-sampling" process by which females use EPCs to assess the quality of potential mates prior to divorcing their current partner. A research paper titled "Why Does the Typically Monogamous Oystercatcher ...Engage in Extra-Pair Copulations?" answered that question as follows: to identify a better mate.There is, however, an alternative possibility.Maybe EPCs occur particularly when divorce is not an option! Assuming that most, if not all, living things are inclined to "move up" if the option exists, an equally con­sistent strategy would be that if you cannot, and if you are stuck with a part­ner who is somehow inadequate-or, rather, less desirable than someone else who might be available-then try EPCs.

A growing body of evidence suggests, however, that females engaging in EPCs may be trying to pave the way for an eventual switch of partners, strengthening a prospective pair-bond. with a future mate. Spotted sand­pipers, for example, are likely to pair with individuals with whom they have previously engaged in EPCs. Such behavior has been described as a "mate­ acquisition·tactic," and it is employed particularly by females.Similarly, in another bird species, the ocean-going razorbills, EPCs are evidently used for mate appraisal.

—David P. Barash, The Myth of Monogamy, p. 102