Because issues like segregated schools and housing, lack of jobs and opportunity — symbols of history that are a source of pride for some and pain for others — these are not tangential to peace; they’re essential to it. If towns remain divided — if Catholics have their schools and buildings, and Protestants have theirs — if we can’t see ourselves in one another, if fear or resentment are allowed to harden, that encourages division. It discourages cooperation.
Obama’s point is that schools that are segregated based on religious identity tend to reinforce those religious identities. He is not regarding these schools primarily as religious institutions, but as institutions that reinforce religious identity. Given the way in which the conflict in Northern Ireland was characterized by differences of religious identity that were only reinforced by the school structures, Obama’s suggestion makes sense. At the very least, if one disagrees with his proposed solution, one must concede that the role sectarian schools can play in the formation of harmful conceptions of identity needs to be counteracted.
This line of reasoning does not imply that sectarian schools must be utterly abolished, but that successful interdenominational educational efforts, even in a few neighborhoods, could do much to overcome the distrust between Catholics and Protestants in Northern Ireland. Lest we forget, schools are not just places where kids go during the day to be indoctrinated: a school is a project of the neighborhood, and not only will the friendships children form across religious divides help to fortify the peace for the next generation, but the cooperation between parents in that project can help to fortify the peace in the more immediate future.
ETA: I am no expert on Irish politics, nor on educational policy, no more than Obama or most of the other people commenting on this issue as if Obama was expressing the wish that Catholic education everywhere ought to be abolished or even devaluing it generally, and insisting on seeing his remarks in the worst possible light serves to discredit the interpreters rather than the speaker. We have plenty of reasons to criticize Obama without manufacturing one.
I’d like to reiterate that the formation of a religious identity can be a very good thing; it was only in the context of a strong Catholic identity that my faith was able to mature. However, the formation of a Catholic identity cannot be achieved at the cost of making of one’s Protestant neighbor an existential threat, (which seems to be the perennial problem in Northern Ireland). It is not that instilling religious identity is a bad thing, but that it can be done badly, and to horrific effect.
Finally, I need to admit for honesty’s sake that at least part of the reason I’m so intrigued by the idea of integrated schools is that I would be very interested in the wider ecumenical implications if such a cooperation were successful.