I heard this one from a teacher as well when I was very young! And it may well have been the same teacher telling us that blood was made of white blood cells and red blood cells, and I knew from my deep work in relevant fields (paints and crayons) that this combination did not result in blue.
We were told that the arteries carry oxygen rich blood, that was red because of a high iron oxide content, away from the heart and lungs to the extremities of the body. At that point capillaries get involved, and it's really best not to worry too much here. Then the veins carry the oxygen depleted blood back to the heart and lungs to be reoxygenated, and that that blood appears blue through your skin. I think copper may have had something to do with the blue coloration, but that blood is also red in color, even if you managed to pull it directly into a vacuum tube. It just appears blue because of your skin or something.
Oxygenated blood is bright red, whereas deoxygenated blood is a darker red. And it looks blue because blue light doesn’t penetrate the skin as deeply as red light. The ones closer to the surface appear blue while deeper ones are purpleish due to the red light reflecting deeper.