The Long History of Diagonal Comparisons

Bayard in the comments linked to Eunice Newton Foote, the Forgotten Pioneer of the Greenhouse Effect:
In her brief study [in 1856], entitled Circumstances affecting the Heat of the Sun’s Rays, the amateur scientist described an experiment in which she exposed glass cylinders equipped with thermometers to the Sun and attached to a pump to draw air from one and compress it in the other.

Eunice compared the heating and cooling in the two cylinders. She observed, first, that the cylinder with the compressed air heated up more than the other in which the vacuum had been drawn. Second, that the heating was greater with moist air than with dry air.

Thirdly, and this was her great and almost fortuitous discovery—since she also experimented with hydrogen and oxygen—that the greatest degree of heating occurred when one of the cylinders was filled with carbonic acid gas: CO2.

OK, this experiment suggests that some gases warm up more than others when in bright sunlight. This illustrates quite a few interesting things about the properties of glass and various gases - mainly density and specific heat capacity of gases, which is why you get the same result with pure argon as with pure CO2 - but it does not in the slightest illustrate what they claim it illustrates. For clarity, Earth's atmosphere is approx. 1% argon and 0.04% CO2.

Here's an article which - inadvertently - makes the contradiction clear:

How can I see for myself that CO2 absorbs heat?

As an experiment that can be done in the home or the classroom, Smerdon recommends filling one soda bottle with CO2 (perhaps from a soda machine) and filling a second bottle with ambient air. “If you expose them both to a heat lamp, the CO2 bottle will warm up much more than the bottle with just ambient air,” he says.

Fine, it does just that. Now, what's the theory again?

Why does carbon dioxide let heat in, but not out?

Energy enters our atmosphere as visible light, whereas it tries to leave as infrared energy. In other words, “energy coming into our planet from the Sun arrives as one currency, and it leaves in another,” said Smerdon.

True.

CO2 molecules don’t really interact with sunlight’s wavelengths. Only after the Earth absorbs sunlight and reemits the energy as infrared waves can the CO2 and other greenhouse gases absorb the energy.

Woah! Just woah! The theory is that CO2 isn't warmed up by SW radiation from the sun, only by LW radiation from the warm surface? And they think that they can illustrate this by showing how CO2 warms up in sunlight?

If they wanted to illustrate how LW radiation from the surface warms up CO2 (more than N2 or O2), they should put their bottles - including one filled with argon as a control - in the shade, so only affected by LW radiation from the surface. If the CO2 bottle reaches a higher temperature than the others, it would be persuasive. Only they know that this wouldn't happen and so would not support the theory... which is why they don't do it.