The problems we take with us aren't the problem this project addresses---there is one problem we unequivocally leave behind if we successfully colonize Mars.
For all our accomplishments, the human species is one unavoidable planet-scale disaster away from total extinction. We know this class of disaster has happened in Earth's past, and we know we lack the capability to stop it. Colonizing Mars gives the species that much more chance to extend its survival past the terrestrial-impact threshold.
There are myriad other ways we could wipe ourselves out that myriad people are working on. None of them matter if something kills Earth's biosphere (much like this project doesn't matter if something like war kills us off before we succeed). They aren't mutually exclusive.