However, every other job can be continued. Why should people be fired if employers can still make a profit? Minimum wage is like a hidden union that ensures that unskilled workers don't outbid themselves.
In the situation when employer is forced to pay more -- he, usually, would benefit more if he hires more qualified person (for that higher rate of pay). So less qualified (but cheaper) worker will be fired (or not hired in the first place, if you consider long-term effects of minimum wage increase).