Cloning humans isn't only about spiritual concerns, or the idea of stealing the spotlight from God.

Humans have been controlling the breeding of animals and plants for centuries. That would seem to be us stepping on God's toes, tampering in "his domain."

Creating "disposable humans" for organ harvesting or servile labor, a second class being, is something people fear will eventually come about because of cloning.

Would a cloned human have the same rights as a human born in the standard manner? Being cloned, it would be easier to tamper with the genetic structure one way or another.

So also there's eugenics to consider. We've been breeding plants and animals to produce variants and better strains, refining strengths and trying to weed out weakness, but when we turn those same processes on ourselves, things start to get a little...well...Brave New World/Nazi Supermen-ish.