Does it matter if it's man-made?
Yes. Most efforts are aimed at reducing man-made climate change by imposing onerous conditions on the populace. If our fossil fuel use hasn't hurt, then cutting our fossil fuels won't help.
If our fossil fuel use hasn't hurt, then cutting our fossil fuels won't help.
CO2 and methane are known greenhouse gases. Reducing them in the atmosphere will lower warming even if humanity not the main factor in climate change.
It does matter though. The paper claims human CO2 is responsible for 0.01C warming. If that is the case, reducing our CO2 can make a maximum cooling impact of 0.01C which is entirely unimportant.
Of course who knows if these numbers are true or not, but the point is it could matter, and our CO2 could be unimportant in magnitude compared to other processes (which is what the paper argues).
Does it matter if it's man-made? It's more or less known what heats or cools earth, and a fast change isn't good for most species and areas.