Superficially, this means “having to do with the Jesuits” (for example: “a Jesuitical education”). However, there’s a deeper, more pejorative meaning to it.
Dictionary.com includes this definition:
practicing casuistry or equivocation; using subtle or oversubtle reasoning; crafty; sly; intriguing.
Casuistry means using dishonest or misleading reasoning.
So, why is this associated with the Jesuits? From Wikipedia:
[…] the peak of casuistry was from 1550 to 1650, when the Society of Jesus used case-based reasoning, particularly in administering the Sacrament of Penance (or “confession”). The term became pejorative following Blaise Pascal’s attack on the misuse of the method in his Provincial Letters (1656 – 57). The French mathematician, religious philosopher and Jansenist sympathiser attacked priests who used casuistic reasoning in confession to pacify wealthy church donors.
So the Jesuits apparently used very selective, disingenuous reasoning to allow the Sacrament to be administered to wealthy people who would otherwise not be able to receive it.
In researching this, I found another usage by Hilary Clinton in 2008 during an interview with Tim Russert. In response to a statement by Russert, she said:
“Well, you know, Tim, we can have this Jesuitical argument about what exactly was meant.”
This was interesting enough to be called out by a Jesuit magazine, which said:
But the word has a second meaning, which is almost always pejorative and was born of the old anti-Jesuit canard that we can be a little slick with our reasoning.
Why I Looked It Up
From Knowing What We Know, when discussing essay questions in an exam setting:
[…] come up with cogent and coherent and, with luck, non-Jesuitical answers to the examiners’ questions.