Great question. I don't have any objections but I haven't seen enough proof. So far it is not science. We are taking multiple scientific studies, combining them and some are saying "see this is proof". Science doesn't work that way. But I digress...to your two questions.
1) Why did we see higher CO2 in the past but not higher temperatures? To quote the article "it appears that much of the last 550 million years has experienced carbon dioxide concentrations significantly higher than the present day." Much of the theory rides on CO2 and temperature being in a causal relationship.
2) What would make me believe the theory is correct...I have thought a lot about this and I don't think one piece of data will do it. But the first thing I would need is for the models to start matching reality. I want to see the average temperature increase for 1 year, 5 years, 10 years, & 20 years with the variance of accuracy. The more accurate the more interested I will be.
What would convince you that the theory of Global warming was wrong?
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Your statement about 650,000 years is correct but when we look at a longer period of time (see first reference) we see that CO2 was higher.
Quote: "Although contemporary CO2 concentrations were exceeded during earlier geological epochs, present carbon dioxide levels are likely higher now than at any time during the past 20 million years[18] and at the same time [PLEASE NOTE] lower than at any time in history if we look at time scales longer than 50 million years [END NOTE]. NOAA research estimates that 97% of atmospheric CO2 created each year is from natural sources and approximately 3% is from human activities."
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Temperature Data.
There is data and you will notice that the temperature of the earth is at the lower end today when viewed over a 500 million year period. When limited to a 650,000 year period the chart shows a major increase.
http://upload.wikimedia.org/wikipedia/commons/f/f5/All_palaeotemps.png
http://en.wikipedia.org/wiki/Geologic_temperature_record
Even when viewed over 5 million years the increase looks drastic.
http://upload.wikimedia.org/wikipedia/en/6/60/Five_Myr_Climate_Change.png
I don't think the facts I have shown prove the theory either way. But I do think there are enough contradictory facts to question Global Warming. Why was the temperature so much higher? Why was CO2 so much higher but life thrived?
I do appreciate that you are a reasonable articulate person willing to discuss the facts. I know that both sides have crazies (read some of the responses above and below) that aren't willing to listen.