why has evolution favored sexual reproduction using two mates over sexual reproduction using three mates?
Let's break it down: The chance that two individuals of distinct gender meet at one location in space time is tremendously higher than for three. We could do some math here (assuming biased random walks of points in three classes on a 2d surface etc.) but that is not necessary I guess. As far as we know sexual reproduction evolved long before complex sensory systems and/or brains (namely 1250 million years versus 500 million years) that allow for active search behavior beyond chemotaxis. Therefore a random walk would be a reasonable first approximation for organism behavior to simulate the situation back then. Having two genders seemed to have been a good trade-off between the chance to meet and advantages in terms of mixing the genetic information. Note that this answer might not be valid for organisms being able to reproduce in both ways, sexual as well as asexual.