Schools generally teach evolution and the Big Bang because they are widely accepted scientific theories that are supported by a large amount of evidence. Schools generally do not teach intelligent design because it is a religious belief, not a scientific theory. Although intelligent design proponents claim otherwise, there is no scientific evidence to support the claim that an intelligent being created the universe or life on Earth.
Schools are required by law to teach science in a way that is objective and does not promote any religious beliefs. Teaching intelligent design would violate this law because it would be promoting a religious belief in a public school.