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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.
In vertebrates, these molecules are the proteins myoglobin and hemoglobin. Red blood cells (above) contain hemoglobin. Blood is bright red (left), due the presence of oxy-hemoglobin. Hemoglobin (or haemoglobin, frequently abbreviated as Hb), which is contained in red blood cells, serves as the oxygen carrier in blood.