"If mankind lives on several worlds, all kinds of reasons exist for those mankinds to wage wars against each other (one of them being the "Right to be where they went versus the other's lack of that right").
Multiple worlds could shorten civilisation's life span far more than of we were living on one world."

I see little reason why Lunatics would go to war with Martians.

I see lots of reasons why having colonies in Space would prevent wars on Earth.

I do see significant potential for wars with space aliens.
And obviously we could lose those wars.

"Living on one world means being forced to compromise, accept the others and try to live together for the benefit of our children. That sustainable civilzation could take us very far!"

I don't see being forced to compromise and "going far" as ideas which go together.

Is there any example you are thinking about in which being forced to compromise has worked?

"Besides, we don't inhabit the oceans. Why would we want to inhabit other planets?
There's still a lot of room on Earth AND there's also room for sustainable ideas and technologies that will let us evolve and expand our knowledge of the Earth, the Universe and ourselves."

Oh, I agree that there is tons of room on Earth. Earth is underpopulated. Nor is there real a shortage of energy.
No, Space is about opportunity. As is America about opportunity. Unfortunately, even America lacks enough opportunity. How many people in this world lack opportunity? Billions?
It's doubtful that America the land mass, can provide enough opportunity for this world. Space could.