Speaking as someone who has learned this the hard way, over and over and over again, please hear me when I say: "Correct" does not always entail "right", even leaving aside whether being right is even necessarily laudable. Getting all, "Well technically..." in the places where those things disagree is a battle — since it's something to be "won", remember — you'll want to consider carefully whether it's worth fighting, every time.
At some point, I decided that it might be better for all of our well-being, not to have all the "incorrect" people in my life always annoyed with me. Based on the quality of the relationships I now have with them, I think it was worth it. Even better: now, when I do actually make the effort to make these kinds of distinctions, I tend significantly more often to be listened to.
Your mileage, of course, may vary.
EDIT: Phrasing