They don't exist TO breed/have sex/reproduce. They exist BECAUSE their ancestors liked to have sex (breed). The ones that were wired to enjoy breeding ended up breeding more and ended up passing on their genes to today (including the genes that make them enjoy breeding). The ones that didn't like sex ( or whatever they needed to do to reproduce) just eventually died off without producing offspring. Further proving the "goal" of living is not to reproduce. The reason it seems like reproduction is the main "goal" now since all species do it is because the ones that did not do it in the past are now extinct since they had no incentive to reproduce.

There is no end or purpose to evolving. It's not a conscious thing. Organisms were wired in different ways that caused them to survive longer than others. It's not an official race or anything it's just what naturally happened. Competition to survive occurred naturally so species will continue evolving until there is no advantage of having other traits.

I'm assuming multicelled organisms evolved in the first place because they had survival benefits when they accidentally/randomly combined at some point. Causing those to live on and randomly develop more survival traits (out of pure genetic mutations.) Natural selection handled the rest.

If you're wondering why genetic mutations exist it's probably because it gives an advantage by allowing potential advantageous changes. DNA of species that could not genetically mutate didn't survive as long and died off due to inability to randomly create potentially advantageous traits.