Learning to juggle the Truth and Morals is not a skill I particularly have missed.
As for "...learning how to handle detailed, conflicting information under pressure..."
I took that training course while an infantry Marine in Vietnam and later as a Marine pilot.
This is the primary difference between the Lawyer/Politician mindset and that of the Engineer/Pilot/etc. The Lawyer/Politician sees no problem with the fact that they "can be called upon to argue either side at any time, without warning". Concerning dealing with Truth and Morals, the Debate Society tends to "think of it as a sport" and likes to speak of "The skills on the field of battle are what is judged."
On the actual field of battle, Truth matters and, ultimately, so does Morality. "Intellectual development exercise" may enable you to convince the judge, jury & yourself that you are invincible and bulletproof, at least until an unsophisticated, illiterate enemy soldier puts a round through your head.
In a similar vein, the engineers designing a bridge or the wing spar of an airplane are not allowed to play "sport" with tensile strengths, resistance to corrosion and metal fatigue. A pilot who plays fast and loose with his Weight & Balance calculations, Density Altitude vs. Power Developed vs Runway Length will eventually kill himself and possibly others.
When the games of the Lawyer/Politician cause people & society to "crash & burn", during the early stages of the disaster there seldom are roaring flames or towering columns of black smoke as there are for the pilot or engineer. Those come only in the final stages of the disasters caused by Lawyers & Politicians.
rant off
You were right to walk out. You picked the right field for your skills. But it is wrong to cast the skill set of debaters as entirely negative because you had a moment of recognizing that the debate team was not for you. Either set of skills can be used for good or for ill.