Roland could easily guess what had happened next.
After knowing that God's Punishment Army was not the only way to compete with demons on the battlefields any more, the Taquila survivors who didn't want to reduce their own kind to the materials for shells must have caused a great conflict with Alice.
Given that, the Battle of Faiths recorded in the written history of the the church probably is just a story made up to cover the truth of this dispute.
As for the root of this disagreement, it did not just lie in the difference between the faith in God's Punishment Army and that in the Chosen One. At that moment, all the leaders of the Union must have been very clear that neither of the choices was able to guarantee their victory in the war against demons.
