There are multiple ways of looking at that, but I'll try to keep it focused. The Little Ice Age. Why did it stop? For all we know the warming that took us out of the Little Ice Age is still ongoing. Why must there be cooling if our temperature is still within the normal bounds of previous interglacial periods?
Without a higher temperature or higher sea level than the Eemain, what exactly is unnatural about our current temperature?
Yes, but why is the temperature rise explicitly originating from CO2? Is it simply because we have no other answer?
The correlation of CO2 and temperature rise in the 20th century is not enough to determine Sensitivity. I could very well point to motor vehicles and our mass production of paved surfaces absorbing more solar energy and heating our planet through UHI. Would that effect really be too small to matter next to CO2 absorption?
I'd like to understand how there is confidence in this. Simple correlation? Our inability to fully account for natural factors? Because when it comes down to it alternative theories just don't compete?
First thing. I think you should read
this. It may explain my position better than my post have come across to you. It also may give you some areas of the current theory where you would want to investigate more to look for holes.
The reason CO2 is the culprit over the last century is that measurements and analysis show it's the only forcing that fits the global surface temperature signature seen.
We've known CO2 absorbs infrared light since John Tyndall did absorption spectrum experiments in the 1860's.
Starting in the 80's a series of NASA satellites, IRIS, AIRS, AURORA, and others have directly measured an increasing drop in the wavelengths of light that CO2 is known to absorb.
Simultaneous ground measurements showed an increase in the wavelength of light that CO2 emits. That reradiated energy warms the globe further.
When the IPCC, NASA, NOAA, et al measured/calculated the forcings they found that all of the increase was described by the increase in CO2 and to a lesser extent methane.
So I'm not saying natural variation can't make a global surface temperature signature the looks like the last century. I'm saying the data indicates natural variation did not while CO2 did.