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Human blood is red because of the iron in the haemoglobin. This gives red blood cells their red colour. Veinous blood is much darker than arterial blood, and your teacher is right that oxygenated (arterial) blood is 'redder' than deoxygenated (veinous) blood. However, human blood is not blue. Some animals do have blue blood though.
Pink/Red from Blood: In good light, press your palm firmly with 1 thumb & hold for several seconds. Release quickly & watch. The return of pink is blood returning into the capillaries; a body wide issue.