Final answer:
The legal issues over teaching creationism in US public schools focus on separation of Church and State and creationism's non-scientific nature. Creationist theories are seen as religious beliefs and not scientifically testable, making them inappropriate for public school science education.
Step-by-step explanation:
The legal battle over the teaching of creationism in US public schools has revolved fundamentally around two major arguments: separation of Church and State and the non-scientific nature of creationism.
The concept of separation of Church and State is deeply rooted in the First Amendment of the U.S. Constitution, which prohibits government sponsorship of a particular religion.
This principle has been central to court rulings that prevent the teaching of creationist theories in public schools, as these theories are seen as a form of religious belief. The non-scientific nature of creationism and intelligent design also plays a crucial role in these legal debates.
Both lack the empirical underpinning required of scientific theories and therefore do not support testable research programs, rendering them unsuitable for a public school's science curriculum which demands factual and testable content.
Teaching creationism or intelligent design is not in the public interest because it does not contribute to our understanding of the natural world in a way that science does.
Teaching these explanations violates the establishment clause, leading to a consensus that they are not appropriate for inclusion in a science curriculum within a public educational system that is required by law to remain secular.