Will removing impacted wisdom tooth on one side affect jaw structure/facial symmetry? why?

Definitely Possible: When you extract a wisdom tooth from one side of the mouth, but not the other, you are creating an asymmetry. That asymmetry can manifest by changing the midline of your teeth in that arch, upper or lower. That happens by "crowding" teeth to one direction. In most cases your dentist should help you understand this phenomenon. Each circumstance is unique, ask your dentist about your particulars.

No: Teeth want to erupt and to migrate forward toward the midline. There's no mechanism for uneven front teeth to unravel back into a wisdom tooth extraction site, nor will removing a wisdom tooth allow the dental midline to shift. Please talk to qualified oral surgeon about consequences of wisdom tooth removal and qualified orthodontist about facial symmetry.

Personally,: In over 40 years of practice, I have never seen that occur nor can i conceive of that happening. The wisdom tooth is within bone and removing the wisdom tooth, no matter how badly impacted, unless there is some major accidental loss of a chunk of your jawbone, should have no affect on facial symmetry.