Cause of lateral inversion: In a plane mirror, the image is as far behind the mirror as the object is in front of it and that the front of the image and the front of the object face each other. This is the cause of lateral inversion in plane mirror.
The image is flipped horizontally not vertically because, you see, the reason that thingsappear to always be flipped horizontally in the mirror is because we flip them horizontally. Try holding up that "Food" sign again, but then flip it vertically to face the mirror, and then you'll see an upside down, but forward facing, "Food" staring back at you.