Q - If two people love each other and know they will get married, then why does the Church say they shouldn't live together?
The analogy that is most commonly used is that cohabitation is like taking a car on a "test drive". The problem is that when we use people as objects, it is the worst thing we can do in a relationship. Pope John Paul II said the opposite of true love is use. This is because we make them less than human when we use them. So, when we cohabitate we are using them in every respect, whether it be for sex, companionship, intimacy, good feelings, etc. - because true love is wanting the best of someone regardless of the cost to yourself.
Putting a relationship in such a "danger zone" is never loving. It basically is saying to the other person (or more than likely to each other) - I see you as useful to me at this time and therefore I am willing to take a risk in hurting you physically (pregnancy, disease, etc), emotionally, spiritually and relationship-wise. Thus, cohabitation can never be about love.
This is the reason that couples who cohabitate before marriage divorce almost double of non-cohabiting couples. Marriage should be a permanent state - for Christians it is a covenantal and sacramental bond that is irrevocable. This permanence along with faithfulness offers a safe environment for real sacrificial love to grow. When a relationship can be changed like a shirt, love can't grow to it's fulfillment.
To make yourself a true gift to someone is the point of marriage. When you cohabitate, you are only able to give a partial gift - which points the relationship down a dead-end street.
A partial commitment is no commitment.
Another big thing to consider for Catholics is that a cohabiting couple may not be able to validly marry. This is a very serious consideration.
Related topic - Top 15 Ways to Mess Up a Marriage.