Friends and Foes
We learn a little more about Richard Highwind, Kain's father in the Nintendo DS remake of Final Fantasy IV. Firstly, that his name was Richard, and also that he died fighting an empire when Kain was a child. This is probably a nod to Ricard Highwind of Final Fantasy II and the first dragoon of the Final Fantasy series.
After Richard's death, the dragoons were in decline. It was the memory of his father that spurs Kain to reject the King's wishes for him to become a dark knight and instead follow the path of a dragoon. Kain mentions his father several times throughout the story, and clearly idolises him. To Kain, his father was the perfect dragoon, a pinnacle of strength and honour. Kain feels like his actions while under the influence of Zemus have shamed him in his father's eyes, and shamed the dragoons, too. It's unclear what age Kain was Richard died, but there's no doubting the huge influence the man has played in his life. The whole reason Kain becomes a dragoon is to follow in his father's footsteps, and even after the evil has been defeated and the world has been saved, Kain is the one who is still not at peace. He goes to Mount Ordeals, to undergo the trial that Cecil did there when he became a paladin. Here, he works to surpass his father, feeling that if he can become a greater dragoon, it would lift his shame and allow him to forgive himself for what he's done.
Cecil Harvey is Kain's best friend. The two, along with Rosa, grew up together, and were close. Cecil clearly respects Kain, and at the beginning of the game seems envious of Kain's decision to turn down learning the dark blade as he did and instead follow his heart to become a dragoon. Even though Cecil - as the Lord Captain of the Red Wings - is in higher standing than a dragoon, he questions his own conscience and worries that he'll soon feel no remorse for the atrocities he's carrying out in Baron's name.
When Kain and Cecil leave Baron at the start of the game, they banter and have a familiar camaraderie. They both have faith in each other's skills. But has much as Kain respects and cares for Cecil, he still harbours feelings of bitterness and jealously towards him due to his relationship with Rosa, and quite possibly due to his higher rank and the prestige of the Red Wings - something which Kain feels should be due to the dragoons. It's these feelings, ones which Kain tries so hard to keep hidden, that allow him to be manipulated by Golbez and cause him to betray Cecil and Rosa in terrible ways. Cecil forgives him immediately, despite everything. Cecil just wants his friend back.
Rosa Farrell is another one of Kain's childhood friends, but his feelings for her run much deeper than friendship. Rosa is kind and is no doubt a good friend, but unfortunately for Kain, that's all he is to her because she fell for Cecil and her feelings for him were reciprocated. Rosa may have known about Kain's feelings, but regardless, she would never have wanted to hurt him.
Rosa gets to play the damsel in distress for a spell in the game. Golbez immediately picks up that Rosa is a weakness for Kain - when Kain is taking one of the Crystals while under the influence of Golbez, it is her voice that gets him to hesitate. This is what causes Golbez to kidnap her, and for the next while all we see is Rosa tied up in the Tower of Zot with Kain keeping guard and watching her most of the time. And while this is a bit of a tangent, I have to say that this actually a trope I really dislike - Rosa loses all her agency and needs to be saved by Cecil. Again. (The first time being when she got sand fever and Cecil needed to go Damcyan to get Edward to go to the Antlion cave to get the thing...you know how it goes.)
...Regardless, despite all this, Rosa - like Cecil - also forgives Kain immediately. Despite what he says about having an awareness of what was going on the whole time, both she and Cecil trust their friend enough to know he'd never act in such a way if he was in control of himself. They both know he strives to be an honourable man, and just wish that he could find a way to forgive himself.
I have read (on the internet so it must be true!) that Kain and Rosa were in a relationship when they were younger. Kain left Baron for a long period of time to train, and she fell in love with Cecil and that was that. This is apparently stated in the Final Fantasy IV Ultimania book, which I don't own and couldn't understand if I did because it would be in Japanese, so I cannot confirm if this is true. However, it's interesting to speculate about, and would certainly add another layer to things and exacerbate Kain's feelings of jealousy, resentment, and anger.