Question

why does the Image in plane mirror suffers lateral inversion?

Answer 1

Because when you are facing north your right hand faces east but your image(reflection) is facing south at that time and thus its right hand faces west.
Short answer: because you and your image are facing opposite directions

Answer 2

The image in plane mirror suffers lateral inversion because the left side of the mirror appears the right of the image and vice- versa, it shows lateral inversion.