Sometimes an event has struck a raw nerve, the customer is convinced to have been wronged and it might trigger some emotional reactions. It is rare that the problem is directly related to you. The customer is not mad at you: they are angry at the situation. Nonetheless, you are the person who can fix the problem and they turn to you.
Take their discontent seriously… But don’t take the negative comments or unpleasant behaviours personally.
Actually, if you want to be professional, it is impossible to do both at the same time.