First rather obvious thing is that building the colony requires a great deal of technological advancement, which in turn creates employment throughout society from research positions to supply chain vacancies. These advancements might also lead to commercial successes which in turn create even more employment and likely an increase in the quality of life.

Second it is a huge inspiration for a lot of people. The very idea that we can conquer space is something that makes me feel shivers. At the same time it is art, testament of the good parts of our species. That romantic notion might end up inspiring many young folk to take careers in fields that contribute to the betterment of mankind.

The bottom of the ocean is perhaps less glamorous, but it's no less technically challenging - the risks of having a permanent base on the bottom of the Mariana Trench would be huge, but we could try living there permanently, growing our own food, conduct research etc - it many ways it's more similar to space exploration than many people think.

There are ways around this, but the moon is a harsh mistress.

This is probably completely ridiculous for reasons obvious to someone who knows what they're talking about.

And where are you supposed to go from the bottom of the ocean? From the Moon or Mars, access to the whole solar system is easier than from Earth's surface.

And importantly, when people say that they want to go to Mars in order to secure the future of our species - the bottom of the ocean is protected form nearly every natural or human made catastrophe imaginable. Even if the surface of the earth was vaporised in nuclear fire, 10km under the surface of water nothing would touch such a colony.

But of course, please don't misunderstand me - of course a Moon colony would be far more preferable.

Living on a single planet is a single point of failure for humanity. A nuclear war, an asteroid impact or a super vulcano eruption and we are done.

(Living in a single solar system is still dangerous, as a gamma ray burst directed at the solar system would still wipe us all out. Leaving the solar system is a lot further out than (trying to) colonize other locations in the solar system.)

But say you are coming back from Mars and want to land on a Moon base or even just dock to a lunar space station. Now you have to brake all the excess interplanetary speed with your engines! And that might be quite a lot, especially if you opted for going faster to reduce the transit time.

But if you are arriving with the same speed at Mars, you can use the atmosphere for aerocapture first without having to brake all that speed with engines. And people might do that for Moon bound trips as well - first do an aerocapture to an excetric Earth orbit using Earths atmosphere and only then adjust the resulting orbit for Moon encounter. That should reduce the raking requirements quite a lot.

For that reason I can imagine future interplanetary ships always having a degree of aerodynamic capability, so they can make use of the atmosphere to slow down when needed. Even if they are not really made to land on a body with atmosphere.

For landing on earth you only need aerobraking and parachutes. For the moon all you need are the retro rockets (we’ve already done it). To send humans to Mars you need retro rockets, a heat shield, and a parachute. The combination of systems makes the whole procedure a lot more complicated and error prone, increasing risk.

[1] http://sicsa.egr.uh.edu/sites/sicsa/files/files/projects/dec...

Still, I think there are definitely cases where atmosphere helps (even if it causes issues elsewhere).

So even if you used propulsive breaking to get captured into orbit of a body with atmosphere for safety reasons, you can still capture into a very eccentric orbit & then carefully use aerobraking (as demonstrated many times at Mars already) to lower and circularize your orbit before landing. And with a bit better aerosurfaces you could even use the atmosphere to tune your orbits inclination as needed.

But it does not attract the same level of excitement as Mars does for some reason. We're already been there so it seems it's been ticked off the list...

It is not because there is less in-situ there. Dr Robert Zubrin makes this case in his books.