To argue for this point of view, think about the implications of simply allowing the Constitution to be "alive." If you take this to its logical conclusion, what is to prevent judges from simply making the Constitution mean whatever they want?
Think, for example, about the idea of finding a right to privacy in the Constitution. This has led to the Supreme Court taking positions that the people who wrote the Constitution would surely never have contemplated. I am referring here to the ruling that abortion (in the first trimester) cannot be banned and to the idea that homosexual acts are protected by the Constitution.
What (you might ask) is the point of having a written Constitution if its meaning can be changed at the whim of judges? Should we not stick to the meaning of the document as written? If we want it to be changed, we are able to change it through the use of amendments. That would allow the Constitution to "live" without running into the problem of having judicial activism usurp the powers of the legislative branch.
So, I would focus on this idea -- that a written Constitution means nothing if it can be changed based on judges' opinions as to how the values of society have changed. If societal values have truly changed, let that be reflected by amendments and by laws, not by the choices of judges.
Please note that I'm not trying to deny the validity of your points. I'm actually just trying to show you the other side so that you can explain it regardless of what you or I might believe.