Why does the president wear a blue or red tie?

The color of tie the president wears is based on what he wants other people to feel when they see him. A red tie represents power and is often worn when meeting with other leaders, specifically those of allied nations, or when trying to come off as the "alpha." A blue tie, is a calming and more peaceful color. The president might wear a blue tie when meeting with leaders of nations with whom there is a lot of tension, or when speaking during a press conference about issues people may not be happy about.

Many things the president does, he does because it's something he was coached to do. Everything from how he speaks and the Words he chooses, to the way he offers his hand for a hand shake. His choice in ties is no different.