Is there no reason to colonize the moon?

No, there is no reason.

It was suggested we might build a base there to send people off to Mars.

Alas. No one’s going to colonize either place. The moon is a vaccum and Mars is poisonous and dead.

Aside from Hollywood, there is no reason to colonize either place. We can and will send robots to do our work of exploration there. Human footprints there are useless except for photo ops.

Why do so many people want to start a colony on Mars rather than the moon?

The moon is closer than Mars. Mars takes longer to get to, would probably cost more to get to, and with how the people are trying to set it up, you would never come back from that planet.

I’d turn that right around and ask are there people that want to start a colony on Mars? Tell all these other-worldly colonist theory people they are all nuts!
Sadly, neither the moon nor Mars are very hospitable environments to even visit, let along colonize. It is not likely to happen on either place. Ever.
We are influenced by Hollywood and science fiction.
I’m here to give you the straight talk. It’s just that: science fiction.
No one is going to colonize anywhere except Earth, and we’d better get our act together here before we kill off people here.

Martian Pipe dream?

There’s no way humans are going to colonize Mars. Hate to burst your bubble.
There’s no organized magneto sphere on Mars to protect people from the sun. It’s why the Martian atmosphere blew away and the oceans evaporated.
For that reason terra forming can’t be successful there, and scientifically no one wants to contaminate Mars with our germs.
We’re just going to have to fix what we’ve got. Star Trek is fiction.