Running everyday can be bad because it can cause overuse injury.
Overuse injuries result from taking on too much physical activity, too fast, and not allowing the body to adjust.
However if you are a seasoned runner and are in great physical shape already then it may not be bad at all to run everyday.
But if you're feeling any pain or soreness from running everyday then you may not want to run everyday.
I run about 4 times per week and then at least everyday take a walk or go jogging to keep myself healthy and fit.
Running is very good exercise but too much running may be bad for you.
As long as you're also walking, jogging, hiking, cycling etc and staying fit then you won't need to run everyday to stay healthy.