Oversimplification (ignores angle of light from object observed to eye), but here:
Imagine standing in front of a mirror, both arms straight out. A photon leaves your left index finger, travels straight to the mirror, and is reflected straight back.
Now imagine photons leaving all your parts, traveling to the mirror, and reflecting straight back.
The question is "Why is it that when you look in the mirror left and right are flipped, but not the up and down?"
When I look in the mirror I see my right hand exactly where it should be, on the right side of the mirror. If I approach the mirror and then touch it, my right hand touches the right hand image in the mirror, as do my forehead and toes respectively.
Someone who asks this question, after understanding what's happening with the light, appears to expect that the left hand with the watch (for example) in the mirror should be on the same side of the mirror as the real left hand with the watch if the observer turned himself 180 deg (away from the mirror). That's a psychological phenomenon, not a physical one, and I don't know why we do that.
One way to answer, then, is that mirrors don't flip anything, our brains do it, and erroneously.
Oversimplification (ignores angle of light from object observed to eye), but here:
Imagine standing in front of a mirror, both arms straight out. A photon leaves your left index finger, travels straight to the mirror, and is reflected straight back.
Now imagine photons leaving all your parts, traveling to the mirror, and reflecting straight back.
That's all.