Why do people say that you cannot let meat thaw all the way out, then refreeze it again?

I do this with my chicken all the time. Because I pre-portion my meat for salads and sometimes when I get home from the store, I don't have time to portion it right away. I don't want to forget about it sitting in the fridge during a busy week, so I'll freeze it, then thaw it, portion it, and refreeze until I'm ready to use it. It helps with my diet that I'm on, and allows me to marinate several single servings of meat, then just pull it out to thaw in the morning and cook when I get home. Why is it dangerous exactly? I never get sick, and I had a butcher tell me it was ok to do with red meat, but I never asked about chicken or other meats.