Why is the moon still out during the day

As it turns out, whether or not we can see the moon during the day depends on the brightness of its light—which is really just the sun's light reflecting off of themoon's surface—and the earth's rotation. In order for the moon to be visible in the sky, it needs to be above the horizon

The moon is still out during the day because even though we can not see it much, it actually depends on the brightness of its light. If you want to go into deeper details it's actually the sun's light that is reflecting off the moon's surface, which is because of the earth's rotation. If you wanted to see the moon during the day, it would have to be above the horizon.