From the footnotes in the OSB:
The rich man's appeal to Abraham as a spiritual father is not rejected. Rather, Abraham accepts this role, calling the rich man son and showing himself to be compassionate even towards the most wretched of men. The great gulf is not a geographical divide, but the complete separation between virtue and wickedness, a separation that cannot be overcome after death. Note that torments have not changed the rich man's heart, as he still sees Lazarus as a servant existing for the sake of his own comfort. Finally, this account by Christ reveals the communion of the saints: a man, not even a believer, calls out from Hades and converses with Saint Abraham!
When I read that, it made me think about the fact that we decide where we are. That God is always compassionate and loves us, but it is we that decide if we want to be closer to Him, or if we'd rather worship ourselves. It points out that he wanted Lazarus to do something for him. He didn't repent and try to get closer, he just wanted comfort.
It is we who decide. I don't think it's something against praying for the dead. When we pray for the dead, not only asking God to have mercy on them but also that they embrace God. I recall a sermon about how heaven and hell are the same thing and it is our relationship with God that determines if it is a warm, loving feeling or a painful fire. Praying for them is, I think, the idea that it is the warm, loving feeling, and not the pain of tormenting fire.
The problem with the rich man is he was unrepentant...he still just wanted what would make him feel better.
Let me add: this is just the way I understand the footnote and the explanation from Blessed Theophylact and I may be way off-course. Forgive me, if I am.