Minimum wage laws must disemploy anyone whose marginal revenue product to the firm is lower than the minimum wage.
Saying it doesn't is indeed like arguing against gravity, actually it's even more ludicrous, it's arguing against math.
Also insomuch as automation is a factor, arbitrarily increasing the cost of labor promotes that very thing. Pushbutton elevators being the famous example. Button operated elevators had been around before they were economically viable. What made them viable was minimum wage laws. Within a few years of minimum wage laws being enacted elevator operators went from being wherever elevators were, to being a boutique affectation of affluence. Now almost nowhere to be seen. Minimum wage laws made it cheaper to buy more expensive pushbutton elevators than hire operators.
Minimum wage laws just cut off the bottom rungs of the ladder.
Further: If minimum wage laws do not cause unemployment it is because there is a government intervention distorting the labor/employer relationship. In an approximate free market cost will be as low as the employer can get away with while attracting labor from other employers true, but high profits in turn attract competition. Equilibrium is achieved when the profits are not high enough to attract more competition. For profits to remain higher than that means there is something impeding competition, which is of course regulation, tariffs, tax code, licensing, and various other means of statutory monopoly protection.
In that situation the firm which is enjoying monopoly profits at the expense of consumers and employees via government action can sometimes absorb the increase in minimum wage because the MRP of the employee has been held artificially high.
However Over time monopoly profits themselves are eroded since all costs, not just labor, tend to expand to fit the profit and profit margins inevitably decline even if you can manage to hold one cost, labor, low. Monopolies thus become increasingly inefficient over time.
So it's only relatively new monopolies that are in the situation that MRP of employees is sufficiently higher than wages for this to occur.