What am I looking for in the moment when that question comes up? Is it the same as what everyone is looking for when they feel afraid, intimidated, terrified ect.... My guess is that people want comfort, which seems like a simple answer.
What does comfort look like? Is it a hug, is it space, is it a cookie, is it a favorite meal, is it time to do a yoga practice, read a book, watch TV or ten thousand other possiblities?
I guess the best we can do, is keep offering the comfort to others and learn what it is they want. Just because we offer the "wrong" thing has nothing to do with us, it just means they need something different. Keep going and see what happens!