Here is the original article A detection of Milankovitch frequencies in global volcanic activity cited in the article as well as an page with an overview of Milanovitch Cycles. I cannot say definitively that Precession causes the problems but that it suggests it is one of the variables which combine to cause the problem. I am also not saying that earth's position or rotations or wobbles are the only causes. The activity of the sun also comes into play. However if we look at the facts:

1. Eccentricity: Earth's orbit around the sun is elliptical ... however it pulses becoming more or less elliptical over a 100,000 year period. "At present the orbital eccentricity is nearly at the minimum of its cycle." Source This means that earth is receiving 20-30 percent more energy than during a glaciation period. In other words Earth has received marginally more energy than last year. At some point when we finally pass the minimum elliptical orbit we will marginally receive less energy per year.

2. Axial Tilt: The Earth's tilt toward the sun ranges from 21.5 to 24.5. Currently the tilt is 23.5 degrees (moving in the direction of 21.5). Source: What Is Earth's Axial Tilt or Obliquity? This means over the next x number of years the winter temperatures will increase and summer temperatures will decrease until the tilt starts to return in the other direction.

3. Precession: Part of the driving force of the axial tilt is precession - the wobble. As the earth tilts one way to the other, there is a particular wobble which accents the issue. Currently the wobble is placing perihelion (closest point) almost on the winter solstice Source. Once again making winters warmer and summers cooler.

Part of the consequence of both the tilt of the axis and precession is that the gravitational influence of the sun is changing pressures on the surface of the planet. If the earth was perfectly smooth, the attraction would be the same no matter what the tilt would be. However as the mass of the planet varies over its surface increased volcanic action also becomes a factor.

I would agree in one sense I deny global warming ... it's darn cold here most of the time (Canadian's would like to see a little warming) but I don't deny the climate is changing. One of our programmers lives in India and obviously it is becoming uninhabitable in parts. Climate change deniers fall into to groups; idiots who refuse to believe that nothing is changing; idiots like myself who believe that we are on the seashore and the tide is coming in. Stepping into the water (producing CO₂ emissions) will get us wet but even if we had stepped back (stopped emissions decades ago entirely) the water would still be at our ankles now.

The evidence that I for this is in the chart you supplied. Temperature has risen and fallen in close correlation with CO₂. You asserted "... it also tells us that higher CO₂ levels lead to higher temperatures. " That isn't the conclusion that other people have.

...by 2003 new data came in and it was clear that carbon lagged behind temperature. The link was back to front. Temperatures appear to control carbon, and while it’s possible that carbon also influences temperature these ice cores don’t show much evidence of that. After temperatures rise, on average it takes 800 years before carbon starts to move. The extraordinary thing is that the lag is well accepted by climatologists, yet virtually unknown outside these circles. The fact that temperature leads is not controversial.
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Just look at the chart you provided. In the time that is just slightly over 100,000 years the temperature drops significantly even though CO₂ remained quite high.

At the onset of the last glaciation the time lag was 8,000 years and the world was cast into the depths of an ice age with CO₂ variance evidently contributing little to the large fall in temperature.
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Just because there is a correlation does not mean there is causality. From your chart we can see that temperature is cyclical. Additionally we can see that CO₂ frequently lags behind temperature.

If CO₂ caused a drop in temperature, the blue line would be to the right of the red line during the Eemian blip in temperature during the Holocene would once again follow a rise in CO₂. I am not suggesting that humans are having no effect on CO₂ but I question whether we can be blamed for the full amount of climate change.

I think that we are currently close to a pivot point in climate although it could continue to increase as indicated by highs during the Eemian period. I believe that we could be entering a relatively cooler period.

During the Little Ice Age, average global temperatures were 1-1.5 degree Celsius (2-3 degrees Fahrenheit) cooler than they are today. The cooler temperatures were caused by a combination of less solar activity and large volcanic eruptions.
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This doesn't mean that some areas will not be hotter and some areas (except where I am) will be colder. Ironically CO₂ may ameliorate the situation. Despite the coldness and wetness this season, the amount of greenery is exploding around here.