And your lawyers would strongly advocate against that.
In most cases they can't/won't tell you because it could open up legal liability. If they say a reason for you, but then hire someone else to whom that reason also applies and you find out, you could sue them. Or you could find a way to twist it into something against a protected class. Too many ways for the company to get screwed.
That's why they all say "we've decided to go another way" or something equally generic.
And he was right, too.
But I broke it down as follows. We received 300+ applications, we filtered down to 100 that were worth even reading in detail. From those we took 50 that we discussed/scored as a group, and came up with 15 people we wanted to interview. Of those we interviewed 10, and of those we interviewed 5 a second time, and 3 a (brief) third time.
"So yes, you did well, and we'd like to keep your name and reach out" (said sincerely). But for him knowing that he didn't screw something up, there was just an even better candidate and he was realistically still in the top 1-2% of applicants was confidence-boosting.
Even one or two sessions can help you a lot - they are trained in pinpointing "soft" issues.