There are decent people, without a selfish hidden agenda, who support increases in minimum wages as a means to help low-skilled workers, and there are other decent people, with the identical goal, who strongly oppose increases in the minimum wage. So the question is: How can people who share the same goals, helping low-skilled workers, come up with polar opposite means that produce polar opposite results?
It all depends on one's initial premise. It would do us some good to make our initial premises explicit and check them against reality. One initial premise is that an employer needs a certain number of workers to accomplish a given task. That being the case, increasing the minimum wage simply means that all low-skilled workers will enjoy a higher salary and employers will have lower profits and/or customers will pay higher prices. With this vision of how the world operates, the logic of increasing the minimum wage as a means of helping low-skilled workers is impeccable.
Another initial premise is that there is no fixed number of workers necessary to accomplish a given task. Employers might be able to substitute capital for labor such as using dishwashing machines instead of dishwashers, automatic elevators instead of elevator operators, self-service gasoline stations rather than full-service gasoline stations, online reservations rather than reservation clerks or relocating their operation overseas. People who share this initial premise can still have concern for the welfare of low-skilled workers but argue that increasing minimum wages will cause unemployment for some of them and deny job opportunities for others. Given their initial premise, the logic of their argument is also impeccable.
Thus, the question to decide is which initial premise best describes how the world operates. Is it the one that says there's a fixed number of workers necessary to perform a given task, or the one that says employers have flexibility in the mix of workers and capital they use and where in the world they can choose to manufacture? I think the latter description more properly describes how the world operates.
Place yourself in the position of an employer and ask: If a worker costs me, say, $7 in wages, plus mandated fringes such as Social Security, unemployment compensation, sick and vacation leave, making the true hourly cost of hiring a worker $9 an hour, does it pay me to hire a worker who's so unfortunate to have skills that enable him to produce only $5 or $6 worth of value per hour? Most employers would conclude that doing so would be a losing economic proposition.