I can't hardly blame Taru for what happen, she's the one who said to Amane about the date, knowing she will come and here again she said they can go all 3 on a date. It's not like she is intentionnaly trying to steal Amane. Reason for break-up is very unclear, like Amane said you can't go stop loving someone in one day but Nene did agree with being friends and still go to the same high school. It's not like she really hate Amane, she just doesn't feel love for her.
In the end, i'm still conflicted with how it should end, i like KouxNene but i'm not really against NenexAmane going back together, especially with Taru who really want the 3 of them being friends.