Atticus says he puts more emphasis on the rights of the individual and his worth then he does on the influence of the family. How do you react to that statement?

One way to react to this statement is realizing where Atticus Finch is coming from when he says this. As an attorney and as a public servant that was once voted into the legislature, he took an oath to defend the rights of the people. Now, Atticus faces the challenge of defending Tom Robinson, a black man accused of raping a white woman. As such, he would definitely need to put more emphasis on the right of the individual than on the opinions and ideals of his own family, and even those of the entire community.
This challenge is even greater due to the racial tension that exists during the trial. On top of the racial tension, Atticus must deal with yet another conflict: Tom Robinson's accusers, Bob and Mayella Ewell, are members of a highly dysfunctional clan that is notorious for the family's chaotic, disruptive, and illegal ways. In Maycomb, where African Americans are considered to be at the bottom of the social hierarchy, are the Ewells to be believed only because they are white?
As a man of higher education than most, Atticus is very aware of these social variables, which greatly affect public opinion and the overall state of mind of the community. His knowledge and experience in these matters are the factors that help him keep his personal views and the opinions of others separate from his immediate task at hand.
His task is to defend a man that is apparently trapped in a very messy situation. Atticus knows how this complex scenario may end. He knows that Tom Robinson is on the losing end even though he has been wrongfully accused. Hence, Atticus also knows that Tom Robinson needs him more than any other defendant ever will. Atticus is the voice of Tom Robinson in a community where Tom, and black people in general, have always been voiceless. The responsibility of such a task is formidable, and only a man as strong in character as Atticus could take on such a challenge. 
Keep in mind that Atticus doing everything to support his client does not mean that he is a rebel that intentionally wants to go against everybody.  Instead, it means that Atticus has the strength of moral character that many people lack. He is willing to put himself in an unpopular position for the sake of giving Tom Robinson the best defense that he can give him,as it is stated in our Constitution. Indeed, Atticus consistently has to endure name-calling, humiliating social situations with Bob Ewell, and even fearing for the safety of his own children. 
All of these things demonstrate that Atticus goes above and beyond his duties because he views Tom not as just a "client", but as a fellow human being that has fallen prey to very dangerous people. Worst of all, Atticus knows that whatever happens, Tom will lose. As such, Atticus is not only the voice of Tom Robinson, but also the little remaining safety and security that the poor man has left in a cruel society.