A camera is comprised of one lens, so you get the entire image in a single direction. We have two lenses, our eyes, and with the distance they are set apart the brain ties the two 'inputs' together to create a field of depth. A mirror merely reflects your vision and both eyes still receive slightly different views of yourself, that why it doesn't look strange.
To add to this, as most people have mentioned already most pictures are usually your true image, since otherwise you will only ever see a reflected version of yourself (You can arrange two mirrors at 90 degrees to eachother and see your real face).
Videos look less 'strange' because the movement creates a false field of depth, since your brain always tries to see them as 3 dimensional pictures.
Here's an idea, if you can somehow get your hands on a
3D camera, take a picture of yourself, and mirror the image. You should see your familiar mirrored self, and realise you don't look that bad at all
Interesting thing - Unless you clone yourself, you will NEVER see your true self in person. And even if you walked past your clone, it'd look so strange and different to how you know yourself, you'd probably never notice them.
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A thing for why your recorded voice sounds different