Should humans be allowed to play god?

How would you define "playing God?" Every time a person cuts down a tree, breeds a new variety of rose, or lights a fire, they are exhibiting a form of control over nature. Human existence isn't possible without altering certain aspects of nature. You can debate the ethical aspects of some of the ways that humans exert "god-like" influence, but advocating all cessation of such activities is advocating human extinction, which is probably something a divine creator wouldn't want.