Mechanics of the Inuyasha love triangle?
The mechanics work like this:

Inuyasha is in love with Kikyo. She is the first human since his mother that treats him well. Despite Kikyo killing him and sealing him to the great tree, he still loves her.

Kagome falls in love with Inuyasha at first sight, but he doesn't like her at all. When he firsts revives from death, he thinks it is Kikyo, but once he figures out she is someone different, he doesn't care for her. 

Due to framing plot reasons, Kagome and Inuyasha have to work together to save the world. Inuyasha slowly starts to warm up to Kagome over time, as she overcomes the dead Kikyo's shadow. Then Kikyo gets resurrected (as a walking dead corpse). This causes Inuyasha's cooling love for Kikyo to flame strongly again, and causing him to be torn between his first love (Kikyo) and has new growing love (Kagome). However, his loyalties are first to Kikyo, so Kagome always loses out when he must choose between them.

Inuyasha's first loyalty is what prevents Kagome from being able to "seal the deal" with him, and is a hurdle she can never overcome as long as the animated dead Kikyo is around. No matter how close Kagome and Inuyasha become over time (in the main series), he will desert Kagome to run off and save Kikyo if he thinks Kikyo is in danger.