To take into account means to think about or consider something for the future, and the context suggests that the agreement did not consider looking into account the possibility of destroying the entire conception he held about his family.
Consider the statement "But the explicit agreement about telling him the reasons behind his condition didn't think ahead to consider the possibility of destroying the entire conception he held about his family.". Is the statement "But the explicit agreement about telling him the reasons behind his condition didn't take into account the possibility of destroying the entire conception he held about his family." false? Yes/no/unknown