There are some interesting things to note about that word choice. Galupo says:
For one last time: Individuals don’t evolve. Populations do. Furthermore, the genetic mutations that may beneficially affect the survival chances of a species occur at the embryonic level. Hence, fully-grown mammals like Barack Obama and Sean Hannity do not “evolve.” They can turn tail and run, hide in bushes and trees, or surrender meekly to predators or, um, change their minds. But they cannot evolve.Obviously, in the biological sense, no individual can evolve. An individual is what it is. Evolution is, as he says, the change in the makeup of the population as some types of individual organisms become less frequent and others more frequent.
I think one motive for the word choice is that in the popular mind, evolution is seen as going somewhere, and that somewhere is seen as "better". (Indeed, the sequence is so well known it's easy to modify it slightly to make a subtle point or a joke.) We're so familiar with the standard "getting more developed with each stage" visual image of evolution that when President Obama announces that his thinking on gay marriage has "evolved" it implicitly conveys an idea that his thinking has reached a higher and more sophisticated level. It taps into the "right side of history" message which many in that movement want to convey. But of course, the idea that biological evolution is a progressive mechanism in which things get better is wrong, and generally speaking in the wider culture it's precisely the secular folks who take pride in being able to face a "cold, undirected process" of biological development who tell us so. And yet, "evolved" is often used as a positive term with implications of progress in that sector of the culture when it refers to anything other than actually evolution.
Another thing worth noting is that people clearly had to do some creative word choice as "changed his mind" clearly did not apply. I find it well neigh impossible to believe that anyone really thought Obama thought gay marriage wasn't a good idea back in 2008, or come to that that Bill Clinton didn't when he signed the Defense of Marriage Act back in 1996. However, announcing that "I've finally decided it's expedient to be honest about what I think about gay marriage" is hardly the sort of headline that a politician wants to win, so a nice sounding word was in order.