Climate modeling and proofs?

The two primary underpinnings of the theory that Greenhouse warming is caused by man are : Correlative relationship between recent atmospheric CO2 contents and estimated (calculated) global temperatures; and predictive modeling that appears to be able to mimic historic trends and which indicates global warming shall result from the continuation of increasing CO2 (climate forcing concept). Convince me please, if you would, that the correlative relationship is causative and not coincidental or a secondary association; and convince me that climate models are reasonably accurate for predictive purposes. As to the former, I find there is a large disconnect between the two parameters, particularly outside the timeframe of the industrial revolution, and I find that the second, at least for short term climate prediction, has a very poor accuracy to date (I am not confusing weather with climate either). Have fun. I know some of you will love to set me straight.