When the mob goes against your wishes you've been overruled. But when the mob (or any entity) makes a decision that results in harm to itself, that was a bad decision. Decision-by-mob is incredibly amenable to this consequence.

Mobs are too easily swayed by rhetoric, appeals to emotion (particularly fear and anger, see the practical lynch mob calling for Clinton's imprisonment at the RNC). We do not permit mob rule in the US for this reason. We created a democratic republic to provide the majority a voice, but to temper it in a way that it would (theoretically) be harder for it to trample on the minority.

EDIT:

Further. I didn't say that it going against my views made it good or bad. I just said when a mob makes a bad decision it tends to go very bad. We're human. We're irrational. It's very hard to set aside our egos. If we make a bad decision, we too often see it through to the bitter end rather than cut our losses. When that decision is made by 100 million people, what's the consequence when it turns out poorly? The vast majority of those people stick with the bad idea. They don't just stick with it, they fight for it. They won't say, "Oops, we goofed. This was a bad idea and we need to change course." They'll say, "Let's stick with it and see if it gets better next year." They may even outright deny the failure of the plan they've chosen.

By removing majority rule, but not to the extreme your sibling suggests I was arguing for with a dictatorship (similar issue, dictator makes a bad decision, we have to kill them to get rid of them). See my paragraph 3. It's not a solved problem. It's not the only solution. But it is a solution, and it works pretty well. We balance the mob against a strong minority voice.