That's derailing: Person A changing the subject from "A hurt B, and B wants it fixed" to "A's life is so hard and people are being so harsh to A" in order to avoid talking about fixing the situation for B, the injured party.

Let's pick an example to make things more concrete. Person B owns a field, and Person A runs trains on a nearby railroad that throw dangerous sparks onto the field. Person B demands that Person A either stop the trains from passing near his property, or else fit them with a mechanism that will prevent sparks. Now Person A complains that the trains are used by low-income commuters who will be forced to pay unreasonably high prices in order to cover these additional costs. Is Person A "derailing the conversation", or is this a valid point? Extra credit: What might influence your answer to this question?