Nope. Firstly, that article doesnt even mention the word cycle, let alone provide any evidence for it. What it does do, however, is argue against many points you make.
For example, water vapour:
In other words, water vapour amplifies the greenhouse effect, but it doesnt cause it.
Also, on CO2:
So the greenhouse effect is caused, in part by atmospheric CO2, which you agree mankind has increased dramatically.
So you failed to prove the point you were asked to prove, and instead disproved two of your most oft-repeated claims. Well done.