Human Trial Is Human Error

Let's face it. When coming up with a cure that looks like it might end a longtime biological threat to mankind, humans naturally will not handle the testing process of the miracle drug. Whether it be the result of a Corrupt Corporate Executive trying to make a quick buck, or a fledgling scientist trying to end the suffering of mankind, he will think that, just because that testing on animals went well, it will have the same results for human trials. Inevitably, it will get worse, ushering in various degrees of Apocalypse How.

Examples of Human Trial Is Human Error include:

Rise of the Planet of the Apes : The ALZ-112, and subsequently ALZ-113, is what gave the apes their superintellegence, and gave the plague that wiped out all of mankind during the human trials.
I Am Legend: In the 2007 film adaptation, it was a cure for cancer that started the zombie apocalypse. It was never made clear whether any human testing was done, but, from the outcome, it is pretty safe to say that the human trials went horribly wrong.
The 2003 film adaptation of Hulk is an inversion of this trope. While David Banner's self-human-testing of a drug that could genetically enhance a soldier's fighting ability didn't cause the downfall of mankind, it did pass the genetic material down to his son, Bruce. Through a stress-induced environment, that triggered a transformation into the enraged and superpowerful being known as the Hulk, which posed a threat to the local populace if not controlled.
In Hollow Man, the invisibility drug works in humans as well as animals, but the antidote fails to make the main character visible again, something that makes him dangerously insane in the long run.
In Serenity, this caused the disaster on Miranda that created the Reavers. Because apparently, their scientists have no stages between "drawing board" and "full-scale field trial".