I can disprove that pretty easily. I accept the reality of CO2 data, and do what I can to help, but I'm not going back to live in a cave, unless everyone else does, too. Whether I have a sailboat or trawler isn't going to change anything. But I can advocate and vote for policies which move us all forward.
I did follow your source link. First thing I noticed was that it was a "for kids" page.
Next, this, under the chart:
"These graphs are based on the Vostok ice core from Antarctica. They do not include the most recent increases in carbon dioxide and temperature caused by humans. Notice the strong connection between carbon dioxide and temperature. "
The point of the chart wasn't to disprove anthropomorphic climate change, but to show that, when we change CO2 concentration, we change the climate. There are multiple links to explain more. And there's another pair of charts:
You may note that the CO2 concentration chart starts out well above the highest value in the one you posted, above. Also, there's this caption:
"Greenhouse gases are at record levels in the atmosphere. For hundreds of thousands of years, the concentration of carbon dioxide in the atmosphere stayed between 200 and 300 parts per million. Today, it's up to nearly 400 parts per million, and the amount is still rising. Along with other greenhouse gases, this extra carbon dioxide is trapping heat and causing the climate to change.
Seems like a pretty iron-clad case to me.
It's always easy to cherry-pick just the one data point which supports one's own position.