The whole basis of the Constitution's system of government is the idea that you have checks and balances. In this system, you have to have branches of government that can interfere with each other. At the same time, though, the branches have to be independent. This need for independence is why judges need life tenure. As the author says
nothing will contribute so much as this (life tenure) to that independent spirit in the judges...
The reasoning here is this -- if the judges can be removed at the whim of the Congress or the President, how will they ever be independent? If they are not independent, they will just do what the Congress or President wants. If that is all they do, how will they protect us from illegal actions by either of the other two branches.