>

When the entirety of the human race is confined to one planet, then all it's takes is one astronomical event to wipe it out. If humans are to persist and survive, they need to eventually colonize other planets.
Mars is the easiest place to attempt it first.
We haven't sent anyone to Mars yet, that's just the long term goal and probably won't take place until we get more infrastructure up into space and the moon.
Rockets do emit carbon dioxide but there are so few of them that it won't make a huge difference, especially in comparison to all the other options for lowering carbon emissions that we have. >

To expand on the second point:
A single ~~average sized~~ large international airport causes more CO2 emissions in a day than every rocket launch on earth for an entire year. >

that makes no sense. source please. >

And rockets launch communication, broadcast and GPS satellites, without which our global shipping industry would also very much collapse.
They also launch weather satellites enabling us to better predict things like hurricanes, or allow us to detect wild fires early.
Research for Space applications has led to countless spin off technologies that make our daily lives possible.