That's really overly simplistic. Poverty is a complex issue, and having a minimum wage versus not is not going to solve poverty. The point that proponents of minimum wage never stop to ask is their basic assumption, that minimum wage actually does help people to make enough to not be pragmatically poor. However, most of the evidence suggests (no it's not black and white) that in fact, minimum wage doesn't actually solve this problem. It seems intuitive that it would, but it's far from being intuitive. Here's a thought experiment. If we could solve people being poor by simply legislating a wage floor, then why not raise the wage to $100 an hour. If it's as simple as that, then everyone could instantly be rich! Why not $1000 an hour? Yes poverty is a problem and no, not everyone can be rich in this far from perfect world. The law of scarcity (the basis for all of economics) is that there is not enough to go around of anything in this world, and the best way to allocate that for almost everything is in a free market. When a government tries to impose artificial price floors or ceilings, it's the same as a basic law of Physics, shortages result. Governments, individuals, companies, everybody, are all subject to this basic law of the universe. Legislating minimum wage does not rewrite this law of economics.
So then ask yourself, if you're not for a $100 or $1000 an hour minimum wage, why is that so obviously wrong to you whereas $7.25 isn't as obvious to you? Don't let the emotion of poor people suffering on the streets cloud your judgement. We can help poor people in many ways, we're just discussing whether minimum wage actually does that, instead of only intending to do that but making people worse off.