Creationism, perhaps unintentionally, creates a serious moral issue. It positions human beings as having God's ordained supremacy over the whole of all other life on Earth.
This has infused Western culture to such a pervasive and unconscious degree that it still operates among people who no longer believe in Creationism.
It allowed us to develop anthropocentric attitudes that allow us to exploit animals with incredible cruelty, pollute the soils, waters and atmosphere, cause the extinction of thousands of species, damage the ecologies of most ecosystems, and generate climate change at a rate faster than evolution can adapt.
It could be argued that humans were given a caretaker role - a responsibility to husband the Earth's life in a responsible and sustainable way - yet, where that does occur, farmers attempt to practice it at the level of economics, not from an empathic feeling for sentient animals. This is slowly changing now that the effects of climate change are beginning to be felt in most places.
A further counter argument could be that other agricultural and industrial cultures have developed similar exploitative practices without having Creationist ideologies, for instance, China and India.
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Another argument against Creationism is that it is a belief in something that is logically impossible.
If God is defined as a non-material sentient being who is omniscient, omnipotent, omnipresent and good, then he knew before creating Creation that Satan would fall, tempt Adam and Eve to disobey and thus that humanity would be condemned to death, painful childbirth and forever cast out of Eden. I can't imagine anything more cruel or tyrannical. He also knew all the other events that would later occur: his destruction of Sodom & Gomorrah, the Flood, and the torture to death of one man for the sins of all others.
To know that evil will inevitably arise from one's creation, and have the capacity to prevent evil and suffering, and yet to still create it would be, in itself, evil. Therefore God could not be both good and omniscient, omnipotent and omnipresent.
Therefore, a God such as he is defined could not possibly exist. Therefore God could not have created the world. The OT and by extension the NT all rest on a idea (the definition of what God is) which is absurd.
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A third argument is that Creationists tend to be authoritarian and prejudiced. (Please treat this argument as a generalisation - meaning it refers to most but not all Creationists. There are, naturally, exceptions in every group of people). They believe the husband has a right to rule over his wife and children. They tend to be highly sexist and racist and practice double standards in almost every aspect of their lives. They are attracted to authoritarian politics, especially right-wing demagogues. They don't see the direct connection between the rich getting richer and the poor getting poorer. Their own families are neither more nor less functional than non-Christian families, being just as statistically prone to neurological, physiological and genetic disorders, diseases, accidents and drugs. They think welfare belongs inside the family without realising that many people don't have functional families, including their own. Statistically, their men have proven to be the ones most likely to abuse their women and children, and even murder them. This argument against Creationism is that authoritarianism and prejudice is inherently damaging. Even on small scales, the damage done via sexism and racism has far reaching consequences for the whole of society.