To take into account means to think about or consider someone or something, but in this context the person is not considering the assertions made about the ability to parent.
Consider the staetement "What I have to do is examine the evidence they have provided and not consider your own assertions of your ability to parent.". Based on this statement, is "What I have to do is examine the evidence they have provided and take into account your own assertions of your ability to parent." a true statement? Yes/no/unknown