Why can we often see the Moon during the day?

Answer: Its orbit puts it in the daytime sky for part of each month

Its orbit puts it in the daytime sky for part of each month ✓ — The Moon takes about a month to circle Earth, so for roughly half of each month it's above the horizon during daylight hours. It reflects sunlight brightly enough to show against the blue sky, especially near its half-moon phases.

Daytime air is clearer, so it shows up better — Daytime air isn't clearer; sunlight scattering in the air is what turns the sky blue and hides the stars. The Moon is simply bright enough to show through that glow.

It glows with a faint light of its own, even by day — The Moon makes no light of its own; all its brightness is reflected sunlight. It's bright enough to outshine the blue daytime sky when it's up.