Don't know if I'm missing something or misreading something. But, Aki asks Shiho if she wants to start dating (which is what Shiho wants right?) and Shiho get mad with her. Why's that? Did she already think they were dating? Then the bit about finding another lover. Does Shiho know Aki doesn't feel the same as her already? It just struck me as weird.
Shiho has loved Aki for quite long, and her feelings are quite intense. Aki is now casually asking Shiho if they should try dating, without confessing her own feelings. This makes Shiho feel like Aki is treating her feelings too lightly. And to Shiho this proposal is an uncertain middle ground between Aki rejecting her, and confessing for real. She doesn't want to get her hopes up. All of that is why Shiho says "don't play around with my feelings".
Aki brings up the possibility that she might date someone else in the future, and asks if Shiho could still be her friend even then. With this, I think she argues that if Shiho's feelings are as strong as they are, then the two of them are not risking their friendship by starting to date now any more than by waiting. I think she's trying to say that it's better to give it a try now than to regret not trying it later.
The real question is why Aki didn't fall in love with Shiho earlier, when they were in the band together.
Shiho was too scared to make the push back then, and then backed down once she realized Aki was crushing on someone else. If she had made Aki look at her in a different light, things could have been a bit different but who knows. Timing is everything and sometimes it just isn't the time for it. Aki is in a different place mentally than she was back then, and so is Shiho. So it's a bit different.
It's also important that Aki fell in love with Yori at first sight. And Shiho was fairly unassertive back then, compared to the more cool Yori, so their relationship started from a place where Aki felt protective of Shiho. Shiho is also the first girl who has confesssed to Aki, so I think it makes sense that Aki's feelings take a different path with her.
