According to Wikipedia's article on Ad extirpanda:
The bull was issued in the wake of the murder of the papal inquisitor of Lombardy, St. Peter of Verona, who was killed by a conspiracy of Cathar sympathizers on 6 April 1252.
This sounds like personal motives (revenge) mixed in with "well, we tried being nice..."
The theological and legal reason was given as follows:
The bull argued that as heretics are "murderers of souls as well as robbers of God’s sacraments and of the Christian faith ...", they are "to be coerced—as are thieves and bandits—into confessing their errors and accusing others, although one must stop short of danger to life or limb."
The following parameters were placed on the use of torture:
- that it did not cause loss of life or limb (citra membri diminutionem et mortis periculum)
- that it was used only once
- that the Inquisitor deemed the evidence against the accused to be virtually certain.
As far as the original repeal, the Oxford Journal of Legal Studies article "Canon Law and the End of the Ordeal" by Finbarr McAuley has in its abstract:
... it will be seen that that decision was a product of a long-standing campaign by Church reformers to secure the spiritual mission of the clergy by establishing a clear division of labour between the ecclesiastical order and the secular world. Finally, it will be argued that the ordeal was abandoned because Church reformers regarded it as irrational and, consequently, that the claim that it only came to be seen as irrational because it was abandoned, should be rejected.