Answer
B and T cells are produced not by other B and T cells, but by stem cells in bone marrow. Because of this, the DNA of mature B and T cells is not a factor in heredity the way it would be for other kinds of cells.
Work Step by Step
For most cell types, as with most organisms, the parent cells are the same type of cell being produced. This means that the DNA of the parent cells is relevant to what DNA will be present in the newly created “child” cells. For some cells, however, such as B and T cells, they are produced from an entirely different cell type not created by mature cells of the same type. This means that it is not mature B or T cells that pass biological information on to new generations of cells, in contrast to most kinds of cells. Similarly, whole living organisms also pass DNA from generation to generation.