Question: If Jesus prayed that we should all “be one” then ecumenism must be possible, right? Otherwise wouldn’t Jesus be praying an impossible prayer?

You are right. Ecumenism is possible precisely because Jesus prayed for it. In John 17:21ff Jesus prayed,

“I pray not only for these, but for those who will believe because of them…that they may all be one as you and I are one…so that the world may believe.”

The key, as in all things Christian, is to unite our prayer with that of Christ so that we are praying “Thy will be done,” instead of “MY will be done,” which we so often seem to do. The theological principle is that of “convergence.” A good image to illustrate this is a wagon wheel with Christ in the center and the rest of us somewhere on the spokes. The idea is to get closer to Christ. Not surprisingly, as we get closer to Christ, we get closer to one another. We still have a ways to go, but as was illustrated by the recent book by Cardinal Kaspar, Harvesting the Fruits, incredible progress has been made in the last 50 years since the Catholic Church entered the Ecumenical Movement. It makes you wonder what progress will be made in the next 50 years.