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Why is the Church called the Church Militant?
The Church is called the Church Militant because it is the Church here on earth which is still fighting against sin and error. It is also called the Pilgrim Church, since its ultimate goal is Heaven, rather than earth.
If we should fall into mortal sin, we do not cease to be members of the Communion of Saints, but we are cut off from all spiritual communion with our fellow Christians as long as we continue to exclude the Holy Spirit from our souls.