There's an excellent Folding Ideas video about this.
Anyway, here's my thoughts on the topic:
The right lesson is to learn to accept help from others when it feels like the world is against you. Cishet white men are the most privileged people on the planet, but that doesn't make them immune to alienation and depression. When you start to feel like you're losing your rights to others (which is really just other people gaining the same privileges you have), it's easy to feel like lashing out is the right thing to do, to take back what's yours. That's not the appropriate reaction.
Reaching out to others who have experienced similar problems as you and asking for advice and support isn't exclusive to cishet white men, by the way; that's just the lens the text uses to look at alienation, therefore it's the primary example I used. I highly encourage people of every background, should they feel they're stuck in a rut and have no idea how to escape, to ask others for help. Knowing you're not alone in your struggles isn't a cure-all for alienation and depression, but it helps to know that you're not alone in your experiences, and other people have gotten through them, just as you can.
Jack seeks help through crafting the personality of Tyler Durden so he can better grasp the "manly" ideal that he's had preached to him since he was a kid. It's a classic pitfall society puts people in to make toxic masculinity easier to spread (keep in mind, toxic masculinity is not exclusively experienced or propagated by men). The actual Fight Club (as it appears in the movie, not the movie itself) can be seen as an attempt on Jack/Tyler's part to recreate the group therapy that, while dishonestly attended by Jack, was working for him and helping him to heal. Problem is, given the Tyler persona is the one who made it, it's a twisted and cruel facsimile of group therapy, where violence is the solution and avoiding talking about your problems (and the group itself) is seen as core to the experience.
