Inuyasha was in love with Kikyo and when you truly love someone, a bad experience from that person can't make the feelings just go away --- BUT that doesn't mean that it won't be tainted.
When he met Kagome, he hated her because he thought she was Kikyo who sealed him to the tree. It's actually possible to hate someone you love. Love ignites hatred.
Over time, Inuyasha was slowly forgetting Kikyo and became close with Kagome. Friendship is the foundation of their relationship. And friendship is a strong one.
Unfortunately, didn't take long, Kikyo was resurrected by Urasue. Yes, Inuyasha got confused. But still, Kagome was in good standing because Inuyasha was already fond of her the time they first discovered that Kikyo was still around using dead souls.
And Kikyo was a changed woman. Her behavior had nothing to do with the little amount of soul she got from Kagome. Remember she reclaimed it in full but she's still very angry. It's normal because she thought she was betrayed by the only man he loved. And change happens all the time to every woman who felt betrayed.
After resurrection, she wasn't the same Kikyo that Inuyasha once loved.
Imagine that in real life.
You only know the person's face and name but everything including her actions and the way she talks was unrecognizable.
Inuyasha remembers the past. The way it felt. Nothing more, nothing less.
Remembering is different from what you actually feel. You may jump back to memory lane at times but it will only last a few moments.
He will never leave Kagome.
BUT, Inuyasha is a good person. He must've felt guilty every time he remembers Kikyo suffered living, died and still suffering alone --- while he isn't, anymore.
He tried to cut tie with Kagome, because he thought he owe Kikyo his own life but can't fully decide to do it. He was hesitant. Then he met Kagome and admitted he shouldn't be having fun because Kikyo is suffering.
Coz he's not suffering. Means he was over his love for her.
Everyone knows the feeling of loneliness when you and the one you love are apart? But he wasn't lonely.
Inuyasha is not suffering.
He is having fun with his new friends, especially knowing that Kagome's around and safe.
One thing I'm sure is he'll be really lonely if it's Kagome who's gone.
He loved Kikyo. It's a thing from his past and a part of him that can never be erased. He wants his first love to be remembered a great woman. He wants to protect her, including her memories.
And watching Inuyasha over and over again made me realized that the 3 of them are all good people --Kikyo, Inuyasha & Kagome.
Kikyo didn't talk much about her feelings but you'll see through her actions that she later made up her mind and decided to not do anything about her feelings with Inuyasha, but instead serve other people.
Also, Kikyo doesn't want Kagome gone. She doesn't want Kagome to replace her as Inuyasha's past as she can't be his future either. She thinks rationally. She and Kagome are the same on that manner. And she love Inuyasha too much she doesn't want him to be lonely.
On the other hand, Kagome gets jealous and all because she's only human but still saved Kikyo a few times. She respect her as the first woman in Inuyasha's life.
1. Kagome didn't let Miroku carry Kikyo to Mt. Hakurei barrier's boundary.
2. She let Inuyasha leave to look for Kikyo's remains.
She's the perfect version of Kikyo.
She's exactly what Kikyo subconsciously wished to be.
Both nice girl.