He didn’t really - the church simply declared that clerics (priests, etc.) were no longer allowed to participate in trials by ordeal. This happened at the Fourth Lateran Council, under Pope
Innocent III.

Ordeals probably originated in small rural communities, where everyone cooperated to keep the peace when crimes were committed. Could God intervene to prevent a burn on someone holding a hot iron, or to make someone sink or float in a vat of water? Apparently, yes, they believed that could certainly happen.

Water and iron were the most common kinds of ordeals but there were others too - there may have been one that involved swallowing bread and cheese. These ordeals came from Germanic law and custom, rather than the Roman laws/customs used by the church. The church was already opposed to these “natural” ordeals as early as the 10th century at least, because they seemed to be sort of tempting God, challenging him to provide a particular response. How could humans tempt God, or change God’s mind? It didn’t fit in with the
church’s teachings.

The ordeal of battle/duelling is another Germanic custom, but not a “natural” one because the combatants were fighting each other, not interacting with the environment. The duel was supposed to show God's favour for the combatant who was innocent/telling the truth, so the church was opposed to that for the same reason, it seemed like they were testing God.
They were also opposed to Christians fighting against other Christians - that was a huge problem in a medieval society full of warrior knights; the Peace of God and Truce of God movements in the tenth and eleventh centuries also developed for the same reason. But duelling was probably a much older custom than the natural ordeals, and it’s kind of a
special case, since it continued to be used long after 1215, long after the medieval period even.

Another reason the church was opposed was that in the 11th and 12th centuries, the canon law of the church, as well as newly-rediscovered Roman law, were being reorganized into coherent collections. There was nothing like trials by ordeal in those, so as far as the church was concerned, there was no legal or religious basis for them. So opposition to ordeals was already well-established long before 1215.

What happened in 1215 was that the Fourth Lateran Council prohibited clerics from participating in them. Ordeals involved interpreting God’s apparent interventions, and participants had to swear oaths on the Gospels, so clerics were required. If clerics
couldn’t participate, maybe people would stop doing them, and they would just
disappear. That’s apparently what the church hoped would happen, but they
couldn’t prohibit them entirely.

And of course ordeals didn’t disappear right away. People could still hold ordeals if they really wanted to, if they felt they could get away with it without any priests helping out. They were
just…less respectable, maybe. Lack of support from secular authorities also helped. The Holy Roman Emperor Frederick II, for example, prohibited the “natural” ordeals on scientific grounds (people float in water because of air in their bodies, not because of guilt or innocence).

Duelling could never really be eliminated because it was a matter of honour and pride, even if participants no longer really thought God was guiding one combatant to victory. Customs for
duelling simply developed without the need for priests to be involved.

So, in brief, the Fourth Lateran Council in 1215 prevented clerics from taking part in ordeals, but it didn’t (and couldn’t) forbid them in general. “Natural” ordeals became obsolete when ecclesiastical and secular authorities became more powerful and could impose written law codes, instead of local communities continuing to use their own customs. The ordeal of battle between two armed opponents probably diminished a little bit too, but it lasted long past 1215, and with guns it lasted up to the 19th century.

Sources:

Paul Hyams, “Trial by ordeal: The key to proof in the early common law," in On Laws and Customs of England: Essays in Honor of Samuel E. Thorne, ed. Morris S. Arnold, Thomas A.
Green, Sally A. Scully, and Stephen D. White (University of North
Carolina Press, 1981)

Robert Bartlett, Trial by Fire and Water: The Medieval Judicial Ordeal (Oxford University Press, 1986)