Some live in a world governed by math. If the cost of an employee is worth more than the added revenue, why would anyone hire that employee? Increasing the minimum wage alters the equilibrium of this equation by requiring larger returns per employee to justify employment. I can prove this on an abacus.
edit: The equation is simply this:
N*W<=\sum_{i=1}^N{R_i}
where N is the total number of employees, R_i is the revenue generated by employee i, and W is the wage paid to each employee. On a per employee basis, we could simply write
W_i<=R_i
If this inequality is not satisfied, then no rational person would ever hire this employee.