Answer – basic economics. Increasing minimum wage has always, and will always, increase unemployment, by the iron laws of cause and effect.
An illuminating discussion from Henry Hazlit, Economics in One Lesson Chapter 18:
The first thing that happens when a law is passed that no one shall be paid less than $30 for a forty-hour week is that no one who is not worth $30 a week to an employer will be employed at all. You cannot make a man worth a given amount by making it illegal for anyone to offer him anything less. You merely deprive him of the right to earn the amount that his abilities and situation would permit him to earn, while you deprive the community even of the moderate services that he is capable of rendering. In brief, for a low wage you substitute unemployment. You do harm all around, with no comparable compensation.
It may be thought that if the law forces the payment of a higher wage in a given industry, that industry can then charge higher prices for its product, so that the burden of paying the higher wage is merely shifted to consumers. Such shifts, however, are not easily made, nor are the consequences of artificial wage raising so easily escaped. A higher price for the product may not be possible: it may merely drive consumers to some substitute. Or, if consumers continue to buy the product of the industry in which wages have been raised, the higher price will cause them to buy less of it. While some workers in the industry will be benefited from the higher wage, therefore, others will be thrown out of employment altogether. On the other hand, if the price of the product is not raised, marginal producers in the industry will be driven out of business; so that reduced production and consequent unemployment will merely be brought about in another way.
Lest he appear to be advocating for low wages, Hazlit clarifies:
All this is not to argue that there is no way of raising wages. It is merely to point out that the apparently easy method of raising them by government fiat is the wrong way and the worst way.
Hazlit’s Economics in One Lesson is well worth reading, especially for beginners like myself. The “lesson” is that we must study all the effects of an action for all people, not just short-term effects for some people. He says:
Economics, as we have now seen again and again, is a science of recognizing secondary consequences. It is also a science of seeing general consequences. It is the science of tracing the effects of some proposed or existing policy not only on some special interest in the short run, but on the general interest in the long run.
If you want to hear a (high school!) student break down the arguments, here’s Sumner Howell: