The very low likelihood of ever living under a lunar atmosphere
As Ernie succinctly it put it back in 1978, “Yes, I’d like to visit the Moon, but I don’t think I’d like to live there.” He then gets a little sidetracked about feelings of loneliness and homesickness, but the core message that the Moon isn’t a terribly hospitable place for humans and Muppets to live is right on. Maybe some details were cut for time, because there’s plenty of ways our Moon just can’t match what you find on Earth, starting with air.
The Moon obviously lacks breathable oxygen, or any of the other key ingredients in air on Earth. This isn’t to say that there are no gasses floating above the surface of our natural satellite, but they’re so sparse that they’re comparable to the amount of gas orbiting the Earth 373 miles above the ground— you know, where people have to live in a space station to stay alive. This area is known as the exosphere, and is the closest thing to an atmosphere our moon has to offer.
Missing mass and magnetism
There are two main deficiencies that prevent the Moon from ever being home to a habitable atmosphere. The first is that as a smaller body, it doesn’t have as much mass as Earth, and thus has a weaker gravitational pull on any gasses nearby (think how easily an astronaut bounces on the Moon, and you can see why an energetic neon atom isn’t going to stick around long.) An object doesn’t have to be huge to hang onto an atmosphere, but it needs to be big enough to provide gravitational completion with its neighbors.
Even if a planet or moon has enough gravity to hold onto an atmosphere, it then needs some magnetic fields to protect it. In addition to all the life-sustaining light and heat we get from the Sun, our closest star also bombards the planet with charged particles usually referred to as solar wind. Those particles can strike and erode atmospheres, basically blowing them away from whatever planet they started at. A strong magnetic field from a geologically active planetary core can act like a giant shield, stopping much of the Sun’s bombardment in space (and making some pretty aurora borealis in the process.) The Moon lacks a magnetic field, and so even if you could deliver an atmosphere to its surface, say by smashing some oxygen-rich comets into it, it would be temporary at best thanks to solar wind.
Basically, Ernie was right. The Moon may be a good place for staging other missions heading deeper into space, but it’d never really feel like home.
Source: Could We Create A Livable Atmosphere On The Moon? by Amy Shira-Teitel, Seeker