Was the reason why Hank hated Sonny so much...

By Jove, I think you've got it. Seriously, a good analysis of the character. There is the thought that Sonny wasn't really his son (Hank claiming Sonny as such because if he didn't, he would have had to acknowledge that his wife had committed adultery), but I like your explanation better.

<<was because deep down, Sonny was a lot like Hank and Hank hated himself?>>

Good interpretation! I think you may be right. I think Sonny was the way Hank secretly wanted to be -- a man who felt emotions, who wasn't a racist. Hank feared this "good side" of himself and hated to see it represented in Sonny. I don't think Hank hated Sonny, either. I think, as you said, he was just afraid of how much like Sonny he truly was. It is said that children act out the unspoken fears or desires of their parents. Sonny was the man Hank wanted to be and was afraid to be (who can blame him, with Buck as a father). After Sonny's death, Hank realized he had to be who he truly was, that not being who he was had twisted him and destroyed his family. Hank had to stop hating himself, his true self, and had to learn to love himself -- and his true self was easy to love.

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Hank didn't have any way to know about love. Buck, his dad, worked hard to make everyone hate him, and the absence of the two women in his life who may have been able to teach him about love, were dead early.

So it may be that Hank didn't hate Sonny so much as he didn't know how to show Sonny he loved him.

Yes, despite all the proclamations of Sonny being like his mother, Sonny was really like his father. Hank's "bigotry" early on was really just a product of his own father. Notice how Hank doesn't care about the two black boys being on his property until Buck goads him into confronting them. Even in the confrontation with the boys' father, Hank's heart really isn't in it to tell them to stay off his property. Hank never had the courage to stand up to Buck, but when Sonny fought back against Hank before shooting himself it caused Hank to waken up to the fact that HE was the weak one who could never fight back against his own father. This is why he quit his job at the prison because that job was a product of him just following in his father's footsteps and not forging his own path.

Just wanted to add a spoiler caution to the subject line to warn anyone who has not seen the film but might be researching it.

You nailed it. You said a lot in so few words.

I thought it was because Sonny was too much like his mother.