>WHY … DO PEOPLE THINK THAT?
Because in order to be fully illuminated the moon must be on the opposite side of the earth from the sun. In this configuration the sun-earth-moon alignment creates higher and lower tides, because the sun pulls water in one direction and the moon pulls water in the opposite direction.
https://oceanservice.noaa.gov/facts/springtide.html
https://colors-newyork.com/why-does-a-full-moon-cause-higher-tides/