Why do you practice courtesy in Tae Kwon Do?

Taekwondo teaches the student to develop positive character traits.

Which is better, to be courteous or discourteous?

Like most martial artists, taekwondo artists (taekwondoka), follow a version of the Se Sok O-Gye, a moral code formulated by a Buddhist monk named Won Gwang in the 6th century AD.

The original Se Sok O-Gye (moral code) consisted of five parts:

事君以忠 -- Loyalty to one's king.

事親以孝 -- Respect to one's parents.

交友以信 -- Faithfulness to one's friends.

臨戰無退 -- Courage in battle.

殺生有擇 -- Justice in killing.

One of the easiest and most basic ways of showing respect is to be courteous. This might also be a way of showing faithfulness to your friends.