> Why not?

Because minimum wage sets the minimum value job that can be done.

> How will it detract from your life that someone else existence is worth living?

Minimum wage isn't minimum standard of living. There's a certain level where minumum wage mostly mitigates lack of bargaining power in low wage labor, but as you get further and further beyond that point, you are raising wages less and causing unemployment more.

If you want to set a minimum standard of living, you want a UBI, not a minimum wage.