>>3752527I could write an essay, but I'll try keeping it short.
They were childhood friends, and Renji clearly had a crush on her, however, soon after joining the academy and when Rukia was taken by the Kuchiki clan, Renji completely stops associating with her, Rukia was a complete outsider to most Shinigami, while Renji and all the other VCs became close Rukia was alone. Renji instead devoted himself to an unhealthy and unrealistic obsession where he would never approach her again until he could beat Byakuya. He didn't even comfort her after the whole Kaien incident.
No, instead Renji rocks up to Karakura town months later, swinging his sword at an unarmed, powerless Rukia, making jokes about how she's going to be executed and just being a cunt.
Even going as far to snide her for wearing 'Human Expressions'
Later on in the Soul Society arc, he doesn't lift a finger to try and help Rukia at first, instead trying to kill the only one who is trying to save her.
Only after 90% of the work is done, does he decide to try and act. He's a bitch with no conviction and I won't forgive him for his slights against her.
I didn't see any real romance between them, they hang out a fair bit and have bro/sis aura about them, Ichigo and Inoue were the only pairing that had real weight, even then it was almost completely one sided until the ending.