It can be surprising that many people believe that the lunar phase is caused by the Earth casting its shadow on the surface of the Moon. Flat-Earthers are no exception. But they take it one step further and use the misconception do “disprove” the fact that Earth is a sphere. They are wrong. The lunar phase is the shape of the sunlit part of the Moon seen from the observer.
On the other hand, the phenomenon where the Earth casting its shadow on the surface of the Moon is called the lunar eclipse. Moon phase occurs all the time and undergoes a monthly cycle, while a lunar eclipse happens only a couple times in a year.
If a flat-Earther insists that the Moon appears in the daytime as “proof” Earth cannot be a sphere, then most likely they think that in the spherical Earth model the Moon phase is caused by Earth’s shadow.
In the daytime, it is not possible for a lunar eclipse to occur; it is not possible for the Earth to cast its shadow on the surface of the Moon. And indeed, it is not Earth’s shadow that causes the lunar phase.