Things that actually help while shooting, roughly in order of effect:
Get further away and zoom in. Close and wide is the single biggest cause of faces looking odd — the nearer features enlarge relative to the further ones, so a head turned a few degrees becomes dramatically uneven. Two or three metres back with a longer lens flattens that out. This one change fixes more "bad photos of me" than everything else combined.
Shoot slightly off a dead-on angle, and pick a side. Straight on maximises the left-right comparison, because the two halves sit side by side for the eye to check. A small turn gives the brain a rotation to explain any difference with.
Soft, frontal-ish light. Hard light from one side carves one half of the face differently from the other and doubles any asymmetry. A window at an angle, or open shade, is forgiving.
Take more frames, and take them while they are talking. You are sampling. Sample more.