I struggle to see what she could possibly gain from this. Heck, even if Kaedae and Aoi had been actual lovers, why would that matter know? Just seeking out misery, that is.
While that would be the most obvious explanation in a romance manga, I just don't see it making a lot of sense with what we were presented so far. Kaede and Aoi were seemingly on very good terms when they reunited (even if they haven't seen each other in a while), while Kaede also claiming that she doesn't want be involved in romance anymore because none of the previous partners accepted her manga dream in the long term - moreover, Aoi was shown as being nothing but supportive so far. So I'm also mildly confused about this supposed mystery we're building towards. If it turns out it's just a past romance and Kaede simply didn't mention it until now, then that will be quite disappointing in my opinion.
The implication (that I think the manga has shown) is that both Kaede and Aoi are not being forthright. It's arguing that they did not actually act cordially except superficially. Kaede's memory of her past with Aoi suggests this (amongst other things). Then of course the fact that Aoi nearly avoided Nananmi's invitation to talk is another. Kaede and Aoi's emotional responses are not meant to be taken at face value, and Nanami realizes this.
This is why she wants to understand their past, she wants to get a deeper understanding of Kaede by having a "true" understanding of what went on in her past important relationship. She senses that they are keeping secrets and probably worries about why that might be. I assume she's more worried that Kaede is scarred by something and how can she help without knowing what's real and what's a facade?
Even if it turns out to be a normal bad relationship ending, or missed love, that will still tell Nanami a lot about Kaede, when Kaede almost never says anything about her past. They've been together for a while and how much does Nanami actually know about Kae? It's natural for her to crave that knowledge from someone she loves. That's part of why it's meaningful, regardless of the outcome.
last edited at Feb 15, 2023 10:40AM