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If this is about the thoughts of the MC while he was speaking with the Mother Superior in the train then we can chalk it up to the MC being an unreliable narrator. From the very start of the story, it was hinted many times that the MC is an unreliable narrator, e.g: contradicting thoughts, contradictory actions, weird dreams, and seemingly poor/blurry memory. Recent events that show this is the therapy session, depraved option during the masked Catherine scene and the cigarette scene with Vixie where he blatantly lies. But even then,in my point of view, what MC thinks during the train part isn't the focus of that encounter. 

What matters is the first impression he gave the Mother Superior during her most cautious phase. The  moment I saw the wiretap scene, everything clicked for me. That first encounter with the Mother Superior where he portrayed himself as a horny, skirt-chasing rookie detective, him exposing his own tricks showcasing conceit, him getting slapped by Teresa further showing a pathetic appearance and him further making a "fool" of himself by then blatantly accusing the Mother Superior. After all of those, the Mother Superior wrote him off as a simple, stupid rookie detective. An incompetent guy. But for the MC this means multiple things:

1. He effectively made the Mother Superior's interest in him decline therefore reducing her cautiousness towards him and lessening the possibility of her sending 24/7 surveillance or worse - a hit- on the MC

2. He managed to inject the wiretap in a person of interest and even got the camera trick to work which gives him another possible lead to pursue in case the first lead goes to a dead end.

3. He pretty much confirms Moe's suspicions about the Mother Superior being a shady character because the Mother Superior herself gave away that she is capable of far more things than a normal Mother Superior's capabilities.

Remember though that all these things are just prerequisites before our MC even has a chance of unraveling the mystery of this convent. He seized the initiative in this case at this moment because after those "stupid" actions of his, he is now truly one step ahead of the Mother Superior and will try to widen the gap under her radar.

And yes he was lucky. But the only lucky part is that the Mother Superior herself decided to approach him instead of 1)sending another person to make contact with him or 2)just quietly continuing her surveillance on his actions. Even if we assume that she was more cautious and did one of the things I said above, this will only delay the MC's investigation and might force him to inject the wiretap to someone else. Now this might open up some interesting alternate scenarios but, in my opinion, this will just prolong the case, increase devtime and bore the players waiting for updates. Same results if the Mother Superior instantly decides to get him killed, MC will somehow survive the attempt and might even get closer to the heart of the case but yea, this will muddy the case early on and depending on what happens, might even change the whole church investigation sequence. 

Now I'm not saying that Moolah's story is 100% perfect. Just like you said, about the Carly and Ryan Elsinger story of Sage's side quest, the MC got kidnapped, woke up from an overdose (based on the two thugs' dialogue) then escaped. Now that part where he got kidnapped makes sense to me because remember he is just trying to find out if Ryan is actually cheating so he was caught off guard when he discovered its much more sinister. But what doesn't make sense to me instead is how come the thugs didn't hunt him down after he escaped. Although it's probably because the Sage side quest isn't finished yet so I'm still positive that Moolah will address that issue in the coming updates.

All in all, I can't really say anything about the 

"you'll know later" story doesn't convince

and the comparison to your teacher's fantasy story but Deviant Anomalies, spoiler alert is a mystery story so expect more of this type of situations where the dev will sprinkle foreshadowing everywhere. I don't understand your statement:

I'm not saying to tell us the whole story, 
but if you leave it to explain 
the "now", "tomorrow"... it will only waste time

because in every detective/murder mystery/conspiracy movies and stories I consumed, the explanations are intentionally withheld from the audience until the big reveal where the protagonist reveals the timeline of events, motives of the involved parties and the evidences that support his conclusion into a final retelling of the true story that happened in one fell swoop.

Moolah provided enough crumbs of information to help the audience see the premise of the main storyline and enough foreshadowing to help the audience arrive to their own theories. And most important of all, MC didn't particularly act out of character and all his actions make plausible sense. Moolah most likely already has the church case finished in story form and that's why he keeps saying that it will be shown later because he doesn't want to spoil it.