Ok, I'm not an expert in Biology - though I do study it - but I think this manga is more accurate and in depth than what would be taught at GCSE level in the UK.
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DanYHKim You're right. Carbon dioxide is actually more soluble in blood than in oxygen. But this way of transport is only 5-7 percent of all the carbon dioxide that is transported.
Another 10 percent is transported by actually binding to the hemoglobin, forming carbaminohemoglobin. This is reversible and therefore it is dissociated from the hemoglobin in the lungs to be taken out of the body.
But the majority is transported through the bicarbonate buffer system, which involves carbon dioxide diffusing into the red blood cells.
So, red blood cells do carry carbon dioxide, but at the same time you're not wrong.