For most of our history as a species, saving face was the most important thing in life, next to sex and not getting eaten by wolves. In fact it was just as important, because the person who lost the respect of his tribe by showing fear was ostracized. In which case he would both not attract any mates and probably get eaten by wolves or killed by another tribe. The fear of looking bad was in fact essential to our survival. That is still the case in many areas around the world. So your fear is both natural and healthy. And it can kill you.
You are betrayed by your DNA and societal conditioning. Your survival in today’s world depends on being able to act in your own interest, despite the fear of how it might look to other people, or even to yourself. Your group, whether they be present or in your head, will not be the ones going to the ER if your epic bike jump goes bad — you are. Your fear of either looking weak or appearing rude will cause you to get into an elevator with a scary stranger and be beaten and robbed. Your failure to run away from the big wave because everyone else is taking selfies will cause you to drown right along with them.
One of the best pieces of advice I got about mountain biking came from a highly skilled rider who told me, “Sometimes you have to have the guts to chicken out”. If your instincts are telling you to not do something, don’t do it! Stop right then. Don’t be afraid to be afraid. You may feel, and look, like a chicken, but so what? In today’s world, your group is no longer so important. I once failed to turn back when I realized I was walking down the wrong street. I stubbornly refused to turn around and was attacked and could have easily been killed. I thought at the time that I was being defiant and brave but I now think that I was too weak to allow myself to show fear, even to myself. So what if I looked scared to this pack of wannabe gangbangers? I didn’t know those assholes and never would have seen them again. As for my own shame about being afraid, those feelings would have lasted maybe 20 minutes instead of 20 years. I have never been the same person since that assault, and it could have been avoided by listening to my reasonable fear. You have no doubt seen many a Youtube video of an assault — often, the victim could have simply outrun the assailant. I’m not saying that’s the right approach for every situation, but sometimes it is. That dangerous situation you face may be the most dangerous one you ever will face. I once had a standoff with a knife-wielding gang kid in the East Bay — had I felt the need to “show him” I would have gotten cut, maybe with serious consequences. I got away as quickly as I could and never once thought I should have done anything else.
No one who has any sense lacks fear. Fear is the warning light on the dashboard of your mind — it is there to tell you when something might be dangerous. Be strong enough to admit when something is too much for you. Be brave enough to chicken out — it might save your life.