Sterile water isn't pyrogen free. That takes much more work to produce. and all injectables are required to be pyrogen free by the FDA.
Nothing draws the attention of the immune system like pyrogens being injected subcutaneously.
When injected along with protein therapeutics, like peptides, this "hyperactivated" immune response not only rapidly attacks pyrogens, but the proteins. The reason one doesn't "have any problems" with sterile water is because the body is so aggressive and effective at getting rid of pyrogens in subq tissue. It's the area we evolved to survive external infection from most effectively.
So now your body is filled with antibodies ready to destroy those peptides, and prepared to do it even more effectively next time.
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