Notso Fantastic: What you say is wrong! Forests are steady state - a mature forest loses just as much carbon as it absorbs! (losing carbon mainly through decomposition). Forests only act as sponges when they are not mature. Nearly all of the worlds forests are mature, and so DO NOT chew through any more carbon than they spit out - they are reservoirs, not sinks.
How many cows would nature have had grazing? Not many! Humans have caused all that methane by creating large stocks of cattle and sheep that would not have been there otherwise! (One partial solution to that would be to affix little pilot lights to the rear of the animals at birth...)
Glueball: Look at the averages - 5x10^11 kg/year CO2 from volcanic activity. 18x10^12 kg/year from all human activities. So humans produce 36 times the amount of CO2 that volcanoes do - it's no use making an arbitrary comparison that no-one can put into context with any accuracy (playing on their emotions, rather than giving hard numbers).
As for whether it is significant? Pre industrial revolution CO2 was 210-350ppm (averaging 280ppm). Now it's more than 367ppm and rising - a definite increase. The computer models that estimate what this will do the Earth's temperature all say it will rise, between 3 and 8 degrees celcius. This will destroy some low levels of the food chain, and hence the global ecosystem (including humans) will collapse. No-one knows exactly when, nor how bad the collapse will be, but it will probably be extremely ugly - I personally think a war over food and water will kill most of the human population. War is extremely unpleasant.
So yes, it is significant, but no, it is not exact.