Why is the moon out during the day?
The Moon is bright enough to be seen even in daylight most days.
The Moon goes through its 29 day cycle from new moon to full moon and back to new moon.
The Moon's axis is also inclined at about 5 degrees, so it is only visible in one hemisphere most of the time.
The Moon is bright enough to be seen during the day from somewhere on Earth as long as it isn't too close to new moon or full moon.
For a few days around new moon the moon isn't bright enough to be seen during the day.
For a few days around full moon the Earth gets in the way so it can only be seen at night.
So, in fact the Moon can be seen in the day from somewhere on Earth most days.
It is a little know fact that if the conditions are right and you know where to look you can see Venus during the day.