Daytime moon
Can the moon be up in the daytime?
Yes. The moon is above the horizon about half of every day, and those hours drift through daylight as the month goes by. It is simply bright enough to beat the blue sky. On the day/night map the pale marker is where the moon stands overhead — watch it ride through the lit half.
The moon does not know about night
The moon goes around Earth once a month. For about twelve hours of every twenty-four it is above somebody’s horizon, and those twelve hours slide through the clock as the month goes on. Roughly half of all the time the moon is up is daytime.
You notice it more at night because the sky is dark. In daylight it is still there — a pale disc, bright enough to beat the blue. A crescent is hardest to spot; a fat gibbous moon in the afternoon is easy.
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Where the map puts it
The pale marker on the day/night map is the sublunar point: the one place the moon stands straight overhead at the instant on the slider. It is the same idea as the yellow subsolar point, solved from the moon’s position rather than the sun’s.
Near new moon the two markers sit close together, both in the lit half — that is a daytime moon. Near full moon they sit on opposite sides of the world, so the moon is overhead at night. Press Play and watch the pale marker sweep; it will cross into daylight and back out again.