Wick Birnam would do anything for his brother. That's a good thing, right? Unfortunately, Wick learns too late that this tendency can be counter-productive when the brother in question happens to be a raging alcoholic.
Wick, Meet Flame
In contrast with Don, Wick seems like a tightly controlled man. Think of him as the Type-A personality to Don's Type-B ("b" is for "booze"). We don't know what he does for work, but based on his nice suit and fancy apartment, we'd wager that the guy does pretty well for himself.
For his part, Don feels emasculated by this dynamic:
DON: Let's face reality. I'm thirty-three, living on the charity of my brother, room and board-free, [...] all out of the bigness of his heart.
As we learn over the course of the movie, Wick even used to pay for Don's booze, but has since closed his tabs with local shopkeepers. This is important for two reasons: a) it shows that Wick once directly supported Don's habit, which is insane, and b) it shows that he doesn't totally understand the extent of his bro's addiction.
At His Wick's End
Don's decision to get drunk instead of going on the weekend getaway is the last straw for Wick. He decides to leave without him, but before he goes, he complains to Helen about the hopelessness of Don's situation. Check it out:
WICK: Who are we fooling? We've tried everything, haven't we? We've reasoned with him, we've babied him, we've watched him like a hawk.
But here's the thing–Wick's decision to leave Don alone is exactly what helps him get better. As long as Wick's there, Don has a shield from the world—he's isolated from the consequences of his actions, whether that entails Wick paying for his alcohol or lying to Helen about his current whereabouts.
As long as Wick is there, Don can't hit rock bottom.
Like Rain on Your Wedding Day
As it turns out, rock bottom is exactly where Don needs to go. Until he knows the full consequences of his actions—until he witnesses the horror of the alcohol ward and experiences the terror of the DTs—Don simply won't take the steps necessary to get better.
Because of this, he can only be saved once his brother, his savior, has abandoned him. Talk about irony.