What's wrong with this though? If someone gives you a bad haircut, you "fire" them and find someone else. If someone messes up your car repair, you "fire" them. Look on Yelp for all the businesses that people have "fired" because of bad service.
Everybody else laid into you and now I am going to as well. That's not the type of characteristic that I want in a person running a country. That's the private equity attitude that "I'll buy the business and fire a bunch of employees and resell the business or shut it down if it's not profitable".
The country isn't a private equity firm. Furthermore, even in business, fear(of being fired) does not produce good results long term. Fear may work once but the effect wears off. You get better results by positive motivation over the long haul.
To add, you can't go around firing everyone when you are running a country, otherwise you end up with half of all Americans on food stamps and/or unemployed. When you run a business, you can fire those employees and let the government deal with them through unemployment and food stamps. When you run a country, you are still responsible for those on food stamps.
In summary, Mitt's moments like these "I like to fire people", "47% of people don't pay income tax", and "I bet you 10 grand", make him come off as a person that dislikes lower and middle class people, especially ones that aren't employed in highly respected industries. To be more specific, he comes across as a person that thinks people that work jobs like , retail service workers and waitresses are lazy and should be fired at the drop of a hat.