Countries should be held responsible not only for their current emissions but also for their cumulative historical emissions, given that greenhouse gases accumulate in the atmosphere over many decades.
They are probably right that the burden should be lighter for developing countries who have not contributed as much carbon in the past, but this is not the reason. I empathize that it is likely not fair that we got to release so much carbon as we developed while they may not be able to. But looking at what was done in the past is a retrospective view of what are essentially sunk costs that cannot be undone.
The point of a change in policy is to change our future lives for the better - a decidedly prospective view. If we agree that global emissions should fall* then it is efficient to reduce them where the burden is lightest. There are two reasons why the burden may be heavier in China. First, because China is growing so fast, the marginal effect of a given carbon emission reduction on GDP could be very well be higher in China. Second, if one believes in diminishing marginal utility, the utility loss from a dollar reduction in GDP in China is likely much greater than the utility loss from the same dollar reduction in GDP in the US. If I give up $5 a week, I buy fewer iTunes and Starbucks coffee whereas a Chinese peasant might miss meals. Either effect would argue for more of the burden to be shouldered by developed countries.
*I am skeptical of a carbon emission mitigation only strategy. Best estimates are that mitigation is very expensive, yielding small effects decades into the future. Alternative temperature reducing “geo-engineering” possibilities, while controversial, hold promise too.