I do not explain. Why degenerate yourself to that argument?
Whenever I increase my rates I am prepared to lose some clients. Pricing is always a complex and fluid issue. With the some client I had raised and lowered, gave and taken, mutually from both sides for mutual benefits. Very important thing is that if you have a good client who gave more than you are paid for, learn to recognize those gestures, be grateful and pay back in some way. On the other hand, with some clients, its time to thank them, bid farewell and have a clean cut.
Same with consumer clients like wedding couples. Recently received a demanding call from a demanding bride, demanding to know why I charge so much (really not much, just common rates), and yet still so much more for album (again really not much, common rates), and yet they have to pay in full before the wedding. If the first point of contact already begin with answering rude questions when we barely know each other... I don't wish to imagine what could have followed. Remember many of us chose this job instead of working for a company is to for the freedom of choice. You can choose to be happy or chose to be unhappy. My simple answer to her is that is how it works. There's nothing I could say more, its not a battle I want to fight nor a client that I want to serve. Life is too short to waste on unhappy dealings and business is too fragile to risk problematic clients. Better to spend the time and effort doing good work for the people who appreciate.