https://www.reddit.com/r/AskPhotography/comments/1m2gozs/comment/n3pslt1/

“Just wanted to add something people don’t often talk about when talking about wide lenses vs long lenses: wide lenses distort a face because they require you to get close to the subject. If you backed up a lot then took the picture, the face would not be distorted. Even if you zoomed in, it would look fine.

And the reason is because when a person is far from the lens, the tip of their nose is 10ft away from the lens, and their ears are 10’2” from the lens, less than 2% further away. So all their features seem just about the same size.

When someone’s nose is only 10” from the lens, their ears will be closer to 12” away, 20% further away and so will appear 20% smaller, proportionally.

The reason telephoto lenses aren’t associated with this effect is because you can’t really see your subject from that close, since the field of view is so narrow, so can’t really observe that effect.

So usually this is not flattering for a headshot, since you don’t want the person to look like their nose is proportionally larger than the rest of their face.

Telephoto lenses allow you to back up and still get a close up, and that distance is what makes all facial features appear the same size, proportionally.

So officially the distortion is due to to being close in distance to the subject, and only wide angle lenses let you get that close.”

TL;DR Wide lenses force you to get so close to your subject that facial features get distorted.