Saying “your idea’s better than mine” is how good teams get built.

Conceding a point in front of other people does two things at once. It gets the group to the better answer, and it tells everybody present that ideas are judged here rather than defended, which is what makes people willing to offer theirs. The cost is a small dent in looking like the one who was right.

Next time somebody in your group has the stronger version, say so plainly and attach their name to it. Leave out the part about how you were nearly there. Then use their idea properly, which is the bit that proves you meant it.