I think there several reasons why presidents want to wear red ties when giving speech. First of all, red refers to power. If the president is wearing red, he may seem more convincing, which helps him to gain more support. Secondly, there is a big comparison between red ties, white shirts and the black suits. They will draw the audiences’ attention. What’s more, red is a sign of aggressive. When the president is talking with leaders from other countries or his competitors, red color can exert pressure on them and imply that “My country and I are powerful, do not play tricks”
For the green ones, I think green represents nature. To be more comfortable staying with his families, and to be not so superior, I suppose the president will put on green ties. Also because green is one of human’s favorite colors, it can make his family life jolly and enjoyable.