I'm not an equestrian person, but the DH rode for many years, and did 3-day eventing until a broken neck (as well as an adamant surgeon and a nervous soon-to-be-wife (me!)) put an end to that. (The neck has been repaired, and no major limb paralysis, BTW. Although the x-rays are a thing to behold.) He ALWAYS unclips on the ride side. When you posed your question, I asked him if it was a horse-related thing, and his response was: probably.
Yeah. Gotta love that definity!
Anyway, his thought was that he probably feels more comfortable clipping out on the ride side because of the horse thing, as he rode horses long before he rode bicycles. But, his follow-up thought was that as long as you are clipping out comfortably, there is no need to change. He will tell you that being able to clip out on both sides is a good skill, there is nothing wrong (or unnatural) with having one side feeling better than the other.
So, go with what feels good, and don't get too stressed about it. So says DH (who has been known to pontificate on occasion!
)
Melior victus per venenum