The majority of interactions between traveler and agent go the way of what you see pictured here -- professional courtesy and efficiency.
But when things go poorly, travel complaints often have a sense of urgency attached: you need to get on the next plane out of town or you need that hotel room you were promised. Under stress, many of us raise our voices and quickly lose patience when we sense someone is less concerned about our problem than we would prefer.
No one is suggesting you become a "pushover" and allow the system to trample you. But make your points with a calm politeness rather than a shrill, demanding tone. Ask for a manager. Be clear about what you think would resolve the situation on the spot. If you need a free room or a refund, ask for it. Don't wait for it to be offered.
Remember that whatever an employee tells you does not need to be the last word. But if they can say truthfully that you were loud, rude or even threatening, you might face even more trouble. At the very least, human nature kicks in and the person on the other side of the counter decides there is no reason to help you.