Bingo for akamomo because I've seen it around a lot recently and it baffles me and I want more perspective. :D
Ok, I'm so glad you asked because I have a LOT of thoughts on this one! At first glance it sound like a crackship, but somehow it makes a lot of sense ? If we only take into account the main story, it doesn't shows much but the light novel and its adaptation make it so much more interesting.
First of all, they are both very smart, the two most intellectual characters in the GOM. At Teiko, Akashi was probably the only one Momoi could have deep and interesting conversation with. It must have been really refreshing for both of them. Midorima is nice and all, but his perpetual need to beat Akashi at something (Shogi, school grades, etc.) must be exhausting at times. With Momoi he could have fully genuine conversation.
In the Replace novel (and it's manga adaptation) Momoi is completely starstruck by Akashi, it's emphasized by the fact that most of the Teiko Era chapters are in her pdv. Every single time Akashi appears or is mentioned she think about how impressive and smart he is (it's really adorable). She has a blind trust in him and his decisions, but despite how highly she thinks of him she always acts normally around him.
Akashi helped her out multiple times, he is very caring and thoughtful towards her, making sure she'll get to play with fireworks with them after their passage at the commissariat, including her when the GOM plays together, helping her find the lipstick her mom want (and those are just the first three examples that came to my mind, the novel are full of them) Which, i concede, the real Akashi is that way toward everyone, but Momoi is usually the one who takes care of others, so this is the only relationship she has where it feels like it goes both ways. Although rare, when Akashi needs help with something, it is shown several times that she is the one he goes to.
Something the fandom seems to completely forget: it was Akashi who discovered Momoi's abilities. It's thanks to his trust that Momoi was able to truly become a player in her own right instead of just being part of the club because Aomine joined. He is the one who shows the most respect for her abilities (who are in my opinion among the most broken in the GOM). He truly thinks highly of her and he praise her several times for it, whether she is here or not.
And finally, they were the two most desperate to keep the team together when everything goes to shit. Both of them are shown very lonely before the team becomes real friends and this is their first experience with a group of close friends. Losing that broke them both in different ways. (yes, other things played a role, but it was a very important factor.) Their friends are the most important part of their lives for both of them.
Kuroko's focus was on basketball and his drive to show them how their way of thinking was wrong regarding basketball.
I'm really sorry for the length, I underestimated how much I like this ship. It's not my favorite ship for either of them, but it's probably my second fave for both. I don't think they would ever date, but if they did, they would be the most perfect, healthiest, cutest couple ever. (And the GOM would be bound to stay friend forever thanks to their combined effort and scheming, perfect)
