In Chapter 6 we learn that the Full Moon (満月, Mangetsu) has powerful effect on Monsters, according to Centorea it is "A night that calls out their instincts with the utmost force." Thus making their passions and behavior more extreme and reducing their self-control.
In practical terms, combined with the possibility of Kurusu being able to marry this caused the girls loose their control and use their strength in full, to the point that he feared for his life.
Amusingly enough, apparently the way to reduce the effects is to literally cool their heads. The morning after, it was shown that the girls have little to no recollection of their behavior.
After learning of this firsthand, Kurusu determined that his home stays must go to bed early on nights with a full moon, and has apparently not had another incident since.
- This is an obvious allusion as to how animals and people are affected by the full moon, bringing out their more bestial and primitive nature.