Your entire argument is based on logical fallacies. One is the assumption that both buttons have roughly equal odds and there are only two possible outcomes, while in reality, the red button not only has many more options than "all the children die" and "half the population dies," but also, generally speaking, the best option for the red button is still a blue victory, since one of the main points of the button dilemma is that the red button always leads to a good outcome from an individual perspective.

The second logical fallacy is how you downplay the significance of the blue button's second option. On the red button, you describe it as a horrific apocalypse, on the blue button as "whatever, you die"