As far as talking about Semblances go, Pyrrha volunteered hers because, let's be honest, she probably discovered it while training. It was just, a thing for her.
So I've been turning this over in my head for a bit and I don't think that's quite right. Pyrrha's secret sauce is how she's fine-tuned her Semblance to fuck up 99.99% of Remnant's Huntsman population. Just about every Huntsman works their Semblance into their fighting style, but its full capability is also their trump card. It's not the kind of thing you casually explain when it's the key to a highly successful athletic career, and knowing the precise name gives you some sense of its weaknesses. It's a huge mark of trust, and you notice it doesn't go past RWBY/JNPR.
Closest I can think of a modern equivalent is talking about your salary/taxes. There's no real taboo to talking about it, and some real benefits if you coordinate, but socially it's weird unless you know the person. Granted on Remnant it probably goes back to pre-kingdom tribal disputes where your special power was the only thing keeping the guy on the next hill from enslaving your village and knowing his would let you do the same in turn, but that's waaaaaaay more worldbuilding than RT'd use to justify a dramatic reveal.
Long digression, but if any of the "Semblance details are highly personal" deal is applicable to RWBY/the quest, then of course Jaune wouldn't talk about it. It might be years before he realizes the Transistor is a creation of his Semblance and not an expression of it. And then... So what? It's not like anyone else can interact with it, and it's completely unreplicable. It might as well be just another power of Jaune's.
Bah. This is a long stream of consciousness thought that just leads to
[X] Not Everything, A Much Briefer History Of- don't talk about everything it can do- fess up to making AI, yes, but maybe keep the whole... you know, 'almost shot an heiress's bodyguard in the face' thing a secret. Among other things.
With a side order of "Wasn't your business and then wasn't relevant."
Maybe I'm missing something, but why don't people want to tell Jaune's family the truth about The Process and The Transistor? What is his motivation to keep it a secret from them supposed to be?
I can understand not talking about Weiss and Ashford (which we should do out of professionality if nothing else) and why people would rather wait to get Ada's permission before we talk about her and Boriah Lee, but why not tell them everything about The Process and The Transistor?
They deserve to know the truth about why Jaune has been having aneurysms, how Cell has been protecting him at great cost to itself, and to have an advance warning of just what kind of changes the future will bring. I don't expect them to fully understand it (especially since I doubt anyone but Jaune is capable of fully understanding it), but I'm absolutely convinced that they'll be able to handle the knowledge and it will leave them better equipped to be able to help out in the future.
You said it yourself--Jaune doesn't understand the ramifications of what he's done. It's been.... what, three hours since he left the hospital? He hasn't even had time to sit down and look at the Cell, much less ask it about preserving the world.
I fully support telling Jaune's family about the Process, even like the day after this (meaning
@Prok gets to write this scenario twice
) but at the moment all he knows is that it's a learning AI that locked itself in a box in his head.
...that's an accurate summary. Can we call the Process the box AI?
Saying this and dropping the mic might be even better though...