Maito Gai hates Haruno Sakura.
Not because of her rejection of Lee. His student is in the springtime of youth, and while Gai is upset that Lee is upset, he knows that the boy deserves better and has plenty of time to realize that and find someone not quite so shallow.
No, Gai hates Haruno Sakura because of the way she treats Hatake Kakashi.
Gai is Kakashi's eternal rival, and that's all Kakashi has in the way of friendships, and Gai knows it. Kakashi had Team 7, but now Team 7 is gone, again, and Gai knows how close Kakashi is to being broken. And furthermore, Gai knows that Haruno Sakura hasn't a clue, and even if she did, Gai is not sure she'd really care. She can't possibly care if she hasn't noticed Kakashi's condition.
If she hasn't noticed how thin Kakashi has gotten.
If she hasn't noticed the lack of Icha Icha Paradise.
If she hasn't noticed the almost desperate quality of the greeting Kakashi always gives her.
If she'd never noticed how much Kakashi cared for his team, and how Kakashi feels as if he failed his team so horribly, and how the separation of Team 7 has hurt Kakashi so badly.
Maito Gai does not hate Uzumaki Naruto. He thinks maybe Kakashi focused a little too much on Sasuke, and Gai cannot blame Naruto for taking advantage of his youth and finding a teacher who could help him discover his potential. Naruto may be the container for the Kyuubi, but he's a good kid. Gai remembers Naruto's anger at Gaara's merciless crushing of Lee's leg, his defense of his friend Hinata—not even one of his teammates—and the way he started Neji's healing process when Gai never could.
Gai also knows that Naruto cares deeply about his important people and would never purposely hurt one of them—and Gai knows that Naruto considers Kakashi one of his important people. After all, it is Naruto who sometimes sends the letters that leave Kakashi in a good enough mood to pull out Icha Icha Paradise and to accept Gai's challenges, even if that mood never lasts long. And even when Naruto doesn't send letters to Kakashi, Gai knows that in his letters to Iruka, he always asks about Kakashi and tells Iruka to make sure to yell at Kakashi if he's late. Gai knows this because he was there once when Iruka told Kakashi what Naruto had said and asked Kakashi if he wanted him to pass along a message. Kakashi wasn't in as good a mood as when Naruto actually wrote him, and most wouldn't notice the difference between the results of Naruto's messages to Iruka and Kakashi's normal attitude. But Gai is Kakashi's eternal rival, and as such, he can tell the difference better than anybody.
So Gai likes Uzumaki Naruto, even if the boy did leave Kakashi for a different teacher.
Gai doesn't even hate Uchiha Sasuke. He thinks maybe he abandoned Kakashi and his teammates, and he thinks that the boy is wasting his youth, but Gai doesn't think Uchiha Sasuke is really completely stable. Gai thinks that Kakashi wasted his time on the brat, but Gai can't hate him.
But Gai can, and does, hate Haruno Sakura.
Haruno Sakura lives in the same city as Kakashi. She sees him often while she studies under the Hokage. But Haruno Sakura never says more than hello unless Kakashi asks her a question. She treats Kakashi, her sensei, who passed her and her teammates when he'd never passed anyone else, who defended his teammates with all that he had, who took D and C class missions as a part of her team when he was capable of so much more, who spent time training her and acknowledged her intelligence and rewarded her for her chakra control, as if he were a mere acquaintance. Haruno Sakura never stops to find out how Kakashi truly is doing. She never stops to notice that Kakashi is slowly falling apart at the seams, and only Gai and Naruto's letters are keeping him together. She never realizes that she is all Kakashi has left Team 7, and when he asks her how training is going, what he's actually saying is, "I'm sorry I wasn't better, I'm sorry I allowed you to be hurt, and I want to know that I haven't completely destroyed you, too. Can you forgive me?" And Haruno Sakura doesn't realize that every time she just answers that her training is going well, what Kakashi is hearing is, "I'm glad to have a better teacher, and I'm glad I don't have to train under you any longer. I can't forgive you for your failures and it was only by chance that you didn't destroy me." She denies Kakashi her compassion and kindness. She fails to see that he might need her to acknowledge him once in a while. She cannot appreciate all Kakashi has done for her.
And so Maito Gai hates Haruno Sakura, for he knows that his eternal rival has been hurt by many things, but it is Haruno Sakura who has broken him.