What a metaphor! I guess this means hiding from things one believes about oneself. Why would you want to distance yourself from these beliefs? Probably because you are ashamed of them. It’s called being in denial.
I think that most of us “run” to one degree or another. The way I tried to face myself was to become introspective and self-aware. I’ve been observing myself for decades now. Some people think I analyze my behavior too much. Some think I’m highly self-aware.
Along the way, I’ve studied a bit of psychology and I’ve been in therapy several times. I’m not sure the therapy helped as much as the theoretical understanding. In any case, I’ve found that close observation (preferably non-judgmental observation) is a good way to keep myself from denying anything about myself, or not seeing it.
When I’m healthy (mentally), I also try to check my observations with others perceptions of me. I ask them what they think about this or that behavior. I try to make myself open to criticism without being defensive. I also ask for advice about how I can do better in areas where I experience difficulties.
The reason why I avoid judging myself or defending myself is that these are techniques for avoiding myself—“running” from myself. I believe that it is helpful if I look at myself as objectively as I can. That means seeing myself as others see me. Sometimes I try to look at myself as if I weren’t myself, but someone else. I criticize myself as if I were criticizing someone else.
This technique has dangers. In an effort to be “objective” I can go overboard. I can start to be more critical than others. I can start to imagine that other people think things; bad things; about me that they do not think. This is why it is crucial to check one’s view of oneself by asking others.
Even so, since I know that I pull my punches with others, I believe they pull their punches with me, even when I ask them to be honest. So whatever they say that is negative, I assume it is actually worse than that. Similarly, since I know it is good to praise people in order to get them to learn and encourage them to exhibit behaviors I prefer, I assume that people’s praise is exaggerated, too.
So, rather than running from myself, I may be harsher on myself than is warranted. At least, from other people’s perspectives. Then again, when I observe myself being harsh to myself, I find that there is some satisfaction I get from it. I do it, I believe, to inoculate myself from criticism. Whatever someone thinks about me that is bad, I think worse. This way, it is never quite as bad as I thought, although it still hurts. I guess pain is safer than feeling good. Feeling good inevitably ends in disappointment and even worse pain.
Of course, self-examination hardly matters if you don’t care what anyone else thinks about you, or you don’t care how they behave with respect to you. In some ways, running from yourself is like ignoring the parts you don’t like. Although, if you do what @Harp suggests, then perhaps you find that there is no need to ignore those parts, since they are illusions, anyway.
It’s hard for me to understand why you’d want to discover your fears to be illusions, since that would seem to lead you to allowing you to run wild, with nothing holding you back, not even harm you cause to others. Then again, maybe the fear that you cause harm to others is merely an illusion. And the idea that other people are angry with you is merely an illusion.