I agree that in a small business that personality clashes can cause a lot of discomfort. A small business is more like a sports team or a close nit family, if you have employees that are being disrespectful or dicks then it'll cause animosity within the "family" and you'll then have a problem with productivity and quality of service as your other employees are not enjoying their work environment.
On the other hand, dismissing someone "cos you don't like them" is a little unjustified and immature.
Work is work, not a playground, as an employee it is your duty to conform to your work environment and as an employer it's your job to create a good work environment to your employees.
I do have to say that I have been subject to being fired cos someone didn't like me. I had a recepionist position in a big transport company before this one. The job was fine till they fired the old office manager and replaced him with a bitch. Unfortunately for me the lady didn't like me one bit. Based on nothing other than character, she was high class and didn't like the fact that I wasn't on the same level as her. She actually took me aside and told me I didn't dress fancy enough or have a good enough hair style to be sitting at the reception desk

(Oh I'm sorry, I left my Gucci/Prada at home today... Bitch) I was going through some health issues then and had spent 2 weeks in the hospital, on my return she sacked me on those terms, taking too much time off work. When it was plain it was just cos she didn't like me.
On my defense, I now work for lawyers that tell me I dress elegantly and make me feel good about the way I look. So she was just being a bitch.
So I can understand a personality clash but when it comes down to the manager/employer just not liking someone for no apparent reason and that being the reason you would lose your job. I do think it's unfair and discriminatory.