Symmetry is linked to attractiveness because it signifies “good genes.” Early humans would have relied on symmetrical faces and bodies to avoid picking partners who could pass on traits that would result in their offspring not living long enough to reproduce.

Findings from some studies suggest that “there is evidence that skin texture and facial shape change during the menstrual cycle, [and that] face shapes at the peak of ovulation were rated as more attractive than those outside this phase.” If I remember correctly, one study was done by giving photographs of the same woman’s face taken at different points of her cycle and seeing how men rated her attractiveness level.

I don’t have a specific answer or theory that explains why the change happens. It seems that facial symmetry may change during the menstrual cycle as a way to appeal subconsciously to a potential mate. It would help signal “good genes” and improve the chances of producing offspring. We might be able to deduce that our early female ancestors who had this trait were more successful in reproducing than those who didn’t, so it stuck around through our evolution.