Because a mirror doesn't reverse anything. The only reversed part is our perception because we compare it to how a person actually standing in front of us would look.
Well, a mirror gives you a different picture than a webcam and a computer screen (unless the webcam software flips the picture along the x axis).
Now why is that, that the software needs to flip along the x axis? It is actually because a mirror mirrors around the the z axis, so it switches front and back.
That is exactly what happens if I open Facetime on my Mac and hold something in the camera.
To be a bit more precise: There are two streams generated. One is shown to yourself, and this one works like a mirror. The other one is shown to remote participants and this one is not flipped.