And before someone says something like "yeah, that's what following the data is all about" or something similar, I agree: plenty of times working at our startups in the past I certainly had to make a business decision I didn't like simply because I couldn't disagree with the data.
So I guess that's a fairly good example, but I'm curious to hear of other examples where you really don't like something -- or perhaps you're opposed to it, for instance, for religious reasons, or simply because of how you were raised I suppose -- but you're nevertheless compelled to agree with it and to support it just because it's the most correct thing amongst all other alternatives.
It could be a philosophical belief or idea; a political view; a social/cultural value or behavior; a legal matter; really just about anything.