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Note that in your own reply, you used the term "theory." A theory is an idea to be tested and proved. A theory is not a fact.
Yes -- a theory in science is a testable hypothesis that explains observations. Sometimes "theory" is applied to things that are completely accepted as fact, such as the "theory of relativity" (this particular theory made a number of predictions which have all been abundantly verified). Sometimes "theory" is applied to things generally accepted as true but perhaps still controversial (the theory of evolution might be an example of this), and sometimes to things which are as yet completely unproved. In the case of our dear departed mammoths, there are competing theories that offer good explanations for their extinction but no convincing test available for eliminating the one theory or the other. I think, however, it is clear that humans were capable of causing the extinction (whether or not they were guilty).
Be that as it may, my original premise was that humans can have no lasting impact on the earth, climate or otherwise. As the earth has continued to survive, even without the presence of Mammoths, then I will stand by my original premise.
By the way, many of these same scientists have a theory that 99.99% of all living species that ever existed on the planet earth are now extinct. If that is true, then any effect man may or may not have on the extinction of species is really quite trivial.