I am going to presume you meant "exit" poverty. And I do care about people exiting poverty. But I am not certain that a price floor on the price of labor is the way for large numbers of people to exit poverty, as it is understood
that price floors consistently produce surpluses. In this instance, a price floor on labor can produce a surplus of labor, i.e., a high degree of unemployment. Perhaps you can show me that unemployment has fallen in areas where minimum wages have increased (and I do not mean short-term unemployment, but long-term unemployment). I am welcome to being convinced otherwise.
I understand. You want people who already work but for less than your ideal minimum wage to be paid more so that they may exit poverty. But I want people who are unemployed to find work. And generally a person who is unemployed for long periods cannot find work because they do not possess a skillset that is in high demand by employers (i.e., at the price that an employer would be willing to pay for their labor). And generally, the way you expand your skillset is on-the-job training. Now, what incentive does an employer have to hire an untrained worker and give them on-the-job training? Well, generally, the untrained employee can offer their labor at a low price; or for free sometimes (see unpaid internships). But when you put a price floor on the price of labor, and make it illegal for the unskilled unemployed to offer their labor at a lower price (which is generally the only bargaining chip they have when negotiating for employment) you make it ever less likely that they will find work unless they can find ways to expand their skillset and thus their chances to gain employment.
After all, would you hire someone at $15.00 per hour if their job skillset means that their productivity would only yield you $7.50 per hour starting out? In other words, you would stand to lose a great amount of money for hiring them? Perhaps if you had absolute faith in their ability to learn, their dedication to the job, and you were absolutely certain they weren't using you as a stepping-stone to a different, better paying job down the line, maybe. But more likely, you would look for someone who is already skilled enough where their productivity exceeds $15.00 per hour in order to make it profitable to hire them. Not because you are malicious or uncaring, but because you do not want to bankrupt yourself.
So I am against such a law not because it will necessarily increase unemployment (though it will for workers whose productivity does not match or exceed the new minimum wage), but that it stands to perpetuate unemployment for a large section of society who will never be able to climb their way out of poverty because they have been priced out of the labor market and employers have largely been disincentivized from hiring them.
