The Daylight Moon

Perhaps they think it is washed out by the Sun. It isn't; if it's up and more than about first quarter it can be seen without any problem if you know where to look. Perhaps they think that it literally is only up during the night, and not during the day. This cannot be true; it orbits the Earth, making a complete circle once a month or so (the word 'month' actually comes from 'Moon'). It orbits in roughly the same path that the Sun follows on the sky, so sometimes it must be between the Earth and Sun, putting it up in the sky at the same time as the Sun, that is, during the day.

I think the answer is more subtle and more telling of how many people live their lives: they simply don't notice what goes on around them. The Moon is easy to see during the day, if people would simply look up! How many times have I seen beautiful rainbows and breathtaking halos around the Sun with multicolor sundogs and found that no one else has noticed? Most non-astronomers I talk to are shocked to find that they can see planets and man-made satellites with their unaided eyes on almost any clear night. But all they need to do is look up and see.