I took this gap to mean one of two things; either I wasn’t being honest with myself, or I wasn’t honest in how I present myself. This bothered me, because I think it is important to be authentically me.

You sound like a good person. I think the fact that you are even worried about being authentic means that you almost certainly are. In my experience, those that are presenting themselves dishonestly do so willfully and usually with a degree of glee at successfully hoodwinking the world. It’s a trail of half-smiles and vapors with nothing at the centre. Trying to find the real person is like walking into a hall of funfair mirrors; it’s as if they’re a character from some le Carré novel.

There’s also the other half of the equation which is not being honest with ones self, but you could also call that not being fair to ones self. Sometimes we can be overly harsh on ourselves when rendering judgement. It can be a surprise when friends rate us higher than we rate ourselves. There is, of course, always the possibility that they might be hopelessly wrong about us :-)