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It's been a while since I watched Supernatural, so don't take my opinions as gospel or anything. But I think Dean is self-hating to the point of narcissism in some ways. Don't get me wrong, I empathise with Dean and understand why fans largely do too. But his self-loathing warps his perception and becomes the centre of EVERYTHING and at times that really has ripple effects on those around him - particularly Sam.
Take their childhood, Sam has a right to mourn the fact that he didn't get a normal childhood. He's allowed to be angry that he didn't get a home, a present father, a stable community, and consistent education. But whenever Sam attempts to express his complicated feelings about his childhood, Dean immediately interprets it as ' oh I was supposed to look out for you. Are you saying I failed? Are you confirming I'm worthless?' which grinds the conversation to a complete halt. Because of Dean's intense self-criticism, Sam can never really be 100% honest with him or ask for support with his own issues, especially regarding their childhood. As anything outside of 100% gratitude just becomes another stick for Dean to beat himself with, and the conversation is immediately derailed.
Not only does Deans self-hatred mean that Sam's expression of his own experiences are pretty consistently shut down. In some ways, I think Dean strips Sam of his autonomy - he's so self-loathing, he sees every decision Sam makes as being about/a reaction to him. A good example of this is Stanford. Rather than understanding Stanford for what it was, an attempt by Sam to carve out a better life from himself and escape hunting. Dean views it as betrayal or abandonment, some re-affirmation of his own belief that he's not worth caring about. Rather than understanding it's a rejection of hunting, he sees it as Sam rejecting him. To Dean, Sam isn't attempting to find a better life, he's punishing the family.
Overall, it's interesting that people largely and rightfully sympathise with Dean due to his self-hatred. However, I don't see as much discussion about how his self-hatred doesn't just hurt him, it hurts those he's close to, as it colours his interpretation of their every action. Dean's self-loathing is always the biggest thing in the room and that has consequences.