Don’t other things matter for climate as well?
They certainly do. Other greenhouse gases also cause warming, while other forms of pollution cause cooling. So far, these effects very approximately cancel out, but this is unlikely to remain so.
Natural factors also play a role, but human influence is already dominant.
Carbon dioxide emissions are the single most important factor in the future and, under all current scenarios, the net effect of other emissions is to add to the warming caused by carbon dioxide. So to limit total global warming caused by human activity to less than 2 °C, we clearly have to limit the warming caused by carbon dioxide to less than 2 °C.