I like the answer (edited for space) from this article:
principiumunitatis.blogspot.com/2009_04_01_archive.html
SETTLING FOR DIVISION AS IF IT WERE UNITY
One of the most common conversations I have with Protestants has to do with unity. I am asked why Protestants are not permitted to receive the Eucharist in the Catholic Church, and why the Catholic Church does not allow Catholics to receive communion in Protestant services.
I explain that the Eucharist is a sign of unity, and so because from the point of view of the Catholic Church, Protestants are in schism from the Church, therefore for Protestants to receive the Eucharist in the Catholic Church, or for Catholics to receive communion with Protestants, would be a lie. In response, the Protestant usually says that Protestants do not see themselves as being in schism or divided from Catholics, but that we are all united in Christ; we all love Jesus and share belief in the essentials of Christianity.
I respond by explaining that there are two different conceptions of unity in use here, because there are two different conceptions of what it is that Christ founded. Protestants generally believe that the church that Christ founded is a spiritual, invisible entity, though some of its members (i.e. those who are still living in this present life) are visible. In the general Protestant mindset, anyone who has faith in Christ is a member of the one church that Christ founded. Protestants generally do not believe that Christ founded a visible, hierarchically organized Body, or that if He did, such a Body is still around.
This Protestant conception of the church as invisible arose in the 16th century. It does away with the very possibility of schism.
The Catholic Church for two thousand years has believed and taught that Christ founded a visible, hierarchically organized Body. This notion of the Church as a visible, hierarchically organized Body has implications for what it means to be in unity. In the Protestant conception of the church as a spiritual, invisible entity,
what counts as ‘the essentials’ is ultimately up to each person to decide. But given the Catholic conception of the Church as a visible hierarchically organized Body, what counts as ‘the essentials’ is determined definitively by the Church authorities. * And what these authorities have determined to be essential includes much more than the lowest common denominator of Evangelicalism. Therefore, from the Catholic point of view, Protestants are not in union with the Church regarding the essentials of Christianity, not only doctrinally, but also regarding the sacraments.*
These two conceptions of the Church, one visible, and the other invisible, also have different implications for what it means to be united in one Body. If what Christ founded is invisible, but has visible members, then the only thing necessary to be fully united to this invisible entity is faith in Christ.
The notion of schism is then reduced to a deficiency in love, insofar as one person having faith in Christ fails to love sufficiently another person having faith in Christ. Unity and schism are then fundamentally spiritual. So given the Protestant conception of the church as spiritual, it follows that if we love Jesus and love one another, we are in full communion, no matter to which religious organization or congregation we belong. By contrast, given the Catholic notion of the Church as a visible hierarchically organized Body, it follows that in order to be in full communion with the Church, one must not only believe the faith taught by that hierarchy, one must be under the authority of that hierarchy.
Some Protestants do claim to believe in a visible Church. But by that they mean that there are many local congregations each with its own visible hierarchy (e.g. head pastor, assistant pastor, deacons, etc.), and that every Christian should be a member of one such local congregation. According to these Protestants, these local congregations need not be part of one catholic (i.e. universal) visible hierarchy. Rather, these local congregations that are each visible hierarchically organized bodies are invisibly united to each other by sharing the same basic faith in Christ and love for Christ. One problem with this position is that its claim that visible hierarchical unity is essential at the local level, but not at any higher level, is arbitrary. If the local church needs a hierarchical organization, then so does the universal Church. But if the universal Church does not need hierarchical organization, then neither does the local congregation. Another problem is that this claim reduces either to the position that Christ founded many Churches, and thus has many Bodies and many Brides, or that the Church Christ founded is itself a spiritual, invisible entity, though some of its members, both individual persons and visible local congregations, are visible.
This is why there is no middle position between the teaching of the Catholic Church that Christ founded one universal, visible, and hierarchically organized Body to which all …
This is also why a Protestant conception of the Church entails apathy about the present disunity of all Christians. Most Protestants see the fact that there is a different denomination represented on every street corner as normal, or even healthy. The very idea that there should be only one Christian institution in every city and all over the world, is completely outside their imaginative horizon, let alone the intended goal of any ecumenical endeavors they might undertake. …
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To our Protestant brothers and sisters we say, "Your vision of the unity Christ intended the Church to have is too small; you’ve settled for division as though it were unity."