Some claim that it's a myth.
And I read an explanation of why some might feel weird around new and full moon.
The moon affects tides,yes?In occult sciences,moon is associated with water element as well.
Moon has effect on water component.And human body is composed of water(around 60%).So,it is likely that moon has an effect on the human body and influence the mind especially during new and full moon when it is in straight line with earth and sun.
The explanation seems like a stretch but it might make sense to some.
https://provinceapothecary.com/blogs/news/how-the-moon-can-affect-you-what-you-can-do-about-it-by-shelly-burton