Why do you want to go to Mars?

I don’t want to move to Mars. It’s a very dangerous environment, you’d be indoors all the time or else wearing a spacesuit for short adventures outdoors. I don’t even think it’s advantageous for humans to go to Mars at all when we could just as well, and for much less expense, send our probes and robot rovers there instead. There is no good scientific reason to go to Mars.
People will go, however, because not everyone is scientifically minded.

Perhaps human race's home was not Earth in the first place, but in another planet, and we came here to prevent extinction

Mechanical, intentional interstellar travel is unlikely since the distances are far too great to imagine. The best anyone could achieve is interplanetary travel within one’s own solar system. Therefore, if we pass the buck and say life didn’t start here but started somewhere else and arrived here, it would have had to arrive on a rock or asteroid as a microbe and somehow survive a fiery entry through Earth’s atmosphere and it would have had to survive the vacuum and temperature extremes of space. If the rock came from outside the solar system it would have had to survive a long, long time.

Would you rather live on Mars or on the Moon?

Since both the Moon and Mars would require a carefully constructed closed airtight environment or else people will die, I’d take the Moon because it’s easier to leave the Moon and go back to Earth if something starts to go wrong. On the other hand, it’s not so easy to leave Mars and go back to Earth.

Partial lunar eclipse
I took this photo from the street in front of my house in Amarillo, Texas, during a partial lunar eclipse. You can see the upper left corner of the moon is darker. The green light in the foreground is a streetlight on Pagoda Drive, Amarillo.

Do we have to go to Mars the way depicted in "The Martian" to succeed in going to Mars?

No. Andy Weir’s “The Martian” was science fiction. It was a possibility, but not a reality at present. Don’t confuse science fiction with reality.
We shouldn’t go to Mars (in my opinion) but we are going anyway. That being said, we have to wait and see how it plays out in reality, not in sci-fi.

lighted hollywood signage during daytime
Photo by Pixabay on Pexels.com