quite the opposite, it makes you stronger as it improves joint health, if you run with good form and have a good pair of running shoes it should be fine to run every day, just listen to your body.you trying to get toned or get bigger? doing cardio is fine but don't over do it. I recommend doing some swimming on days you don't lift to ease your joints.
if you have joint problems or you're over-weight then of course the impact on all your lower body joint is going to destroy you.
swimming is also a superb work out for the whole body, infact running and swimming are the top 2 work outs for strong healthy body.