Hmm I was thinking about it too and i came up with...
After kakashi got his new eye from obito, he felt responsible for obito's death because as their commander/leader, he wasnt able to protect his team, like how Rin got captured by the enemy and wasnt able to prevent obito being crush by a huge rock. And he also felt guilty of what obito said to him about " Those who dont care about their companions are even worst trash" and that made him think about his dad of who he used to look up too, as a child.
Since Kakashi said all his friends are dead, i think he means Obito and Rin or who ever else he was with. So after Rin and others died, he felt even more responsible for their death because in the end he wasnt able to protect anyone but himself. And also Kakashi was highly praise as shinobi and that probably made him think "Since im so great why cant i save my friends".
So thats my theory about kakashi obtaining the MS sharingen, he felt responsible for getting his friends killed because of what he did wrong and couldnt do, since he was the leader and made rash decisions that end up killing his friends....phew that was a long post.. thanks for listening

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