1. It is extremely unlikely that anthropogenic emissions would align so conveniently with the tip of a natural climate cycle. There must be some other factor underlying the correlation, and/or the influence of human emissions is overstated.
2. The argument is that there is an alarming discrepancy between current measured CO2 and historic data derived from cores. However, core data is an estimate based on a number of assumptions regarding capture and diffusion of gasses during and post ice formation, and I have not come across any literature which questions whether ice core derived CO2 values may underestimate historic CO2 levels. Indeed, there are hints from plant data that this may be the case, but publishing such a conclusion would probably be career suicide in the current politicized academic climate.
The first point alone indicates that some natural degree of warming is to be expected at this point in natural climate variations, something which is never mentioned by proponents of climate change. The second point, if true, would mean that the effects of human activity on global climate are over stated and the current evolution of the system is normal, beyond our control, and/or has happened in the past almost exactly as it is happening now.
1. http://www.antarcticglaciers.org/glaciers-and-climate/ice-co...