The minimum wage as it is often advocated is Very Bad Policy.
I’m not saying that because I lean libertarian or because I think it will cost jobs, but because of advocates who are unwilling to weigh costs against benefits and instead deny the costs exist. Understanding that a minimum wage is likely to cost jobs isn’t ideological belief, but the default expectation we should hold if we understand economics.
Theory explains why we expect job losses to happen: If a price floor is implemented on identical goods, some people will no longer choose to pay or be able to afford the higher price, so they’ll buy less and seek out substitutes, even though many people would like to sell more at the higher price.
Most goods aren’t identical, so when a price floor is applied, buyers will be picky. A minimum price for alcoholic beverages means you won’t see much budget vodka or malt liquor on the shelves because few people will pay a premium for them. Those who might enjoy a cold can of, say, Old Milwaukee, but can’t afford the premium price (if it’s offered at all) go without a beer, buy it illegally, or switch to cheaper ways to drink.
Workers don’t sell goods, but services, and people aren’t interchangeable. Some, even if it’s just because they lack training, experience, or education, can do less in any given time than other workers, whether it’s putting things together, keeping track of multiple tasks, or simply working without needing help or supervision.
The minimum wage is a price floor, and it’s people who cannot contribute as much per hour that aren’t as likely to convince buyers to pay for their work. Unlike a can of Old Milwaukee, though, every person is brimming full of potential. Fewer job opportunities means fewer chances to unleash it.
Theory is bolstered by the agreement of most empirical evidence. The evidence isn’t unanimous, but economic theory doesn’t tell us to expect that it should be. When the minimum wage doesn’t eliminate jobs, we can’t declare the general theory to be without merit or we’ll risk treating the exception as the rule. We should explain the exception instead.
But all of that is, emphatically, not an argument against minimum wages. It is only an explanation of one likely cost. Understanding costs allows us weigh them against expected benefits and, if we decide it’s worth it, to choose to bear them and proceed. If advocates of a minimum wage deny costs that we have every reason to expect to make their case, they're asking that we support their policy on false premises. That’s not a good way to make any decision, and an especially bad way to make decisions for other people.
Perhaps, like some people today and the original advocates of a minimum wage, you think that it would be a good way to keep immigrants from taking work from native-born citizens (see point 5 here). More likely, you may look at the costs of the minimum wage and believe that they’re worth bearing because other policies are better suited to improve the lives of low-skilled workers than low-wage jobs. In either case I would disagree, but at least we’d be having the right conversation.