Katczinsky, a.k.a. Kat, is the Mickey to Paul's Rocky, the Obi-Wan to his Luke Skywalker, the Nick Fury to his Iron Man. (Okay, maybe not that last one; Kat's not too big on inspirational speeches.)
Like the famous teachers above, Kat falls into the guide/mentor role. He adopts this persona on Paul's first day at the Front:
KAT: That kind of shell you don't have to pay much attention to. Those big fellows just make a lot of noise and land about five miles behind the line. The things we've got to watch out for are the light ones. They don't give you much warning. They go "waah zing." And when you hear that, down! Mother Earth. Press yourselves down upon her. Bury yourselves deep into her. Just keep your eyes on me. When you see me flop, you flop. Only, try to beat me to it.
You'd think someone might have gone over all this before shipping the new recruits off to war. But Kat's the one who has to teach Paul and his classmates how to survive the war—or, at least, he provides them the skills to increase their chances of survival.
That's Harsh, Man
Kat's unique among the Obi-Wans and Nick Furys of cinematic mentors in that he doesn't tell a budding hero that they're the one destined to defeat evil or save the world. Nope. His lessons are grimmer…but ultimately more useful for a soldier on the lines.
Let's consider Kantorek's lesson to the boys at the film's beginning:
KANTOREK: You are the gay heroes who will repulse the enemy when you are called upon to do so.
This is a lesson straight from the fairy tales. It holds up the mythology of bravery and great victories, where heroic deaths are immortalized in song.
Now let's compare that to Kat teaching Kemmerick the nuts and bolts of how war works. After Behm's killed, Kemmerick runs into enemy fire to retrieve his friend's body. Pretty brave, right? Sounds like something that would make a good story on the nightly news.
But this is what Kat has to say about it:
KEMMERICK: He's dead. He's dead.
KAT: Why did you risk your life bringing him in?
KEMMERICK: But it's Behn. My friend.
KAT: It's a corpse, no matter who it is. Now, don't any of you ever do that again. Put him over there.
That may have harshed Kemmerick's mellow (although we doubt that retrieving the corpse of your best friend is exactly mellow-making), but Kat's right. Behm was already dead. It's not like the enemy could make Behm more dead. All Kemmerick did was risk his own life.
Kat's lessons may lack the luster of Kantorek's rhetoric, but they have one thing going for them: they're 100% true.
Kat's lessons prove so important—and his friendship so vital—that Paul can't imagine what he'd do without his mentor. As he says during their last conversation:
PAUL: It's not home back there anymore. All I could think of was, "I'd like to get back and see Kat again." You're all I've got left, Kat.
KAT: I'm not much to have left. I missed you, Paul.
PAUL: At least we know what it's all about out here. There're no lies here.
The other teacher-figures in Paul's life have taught him lies…or nothing at all. Kantorek taught him that he'd find glory and heroism in the war. Paul's father spoke to him only of honor and victory. And Himmelstoss was only good for learning to crawl through mud. (In his defense, there is a lot of mud on the Western Front.)
But they prove to be spreading lies about the war to anyone who will listen. Kat was always honest and forthright with Paul, and although his lessons may have been bleak, they kept Paul alive and provided him with hope and place to belong.
When Kat's ultimately killed, Paul finds he's lost without his mentor. Losing his hope and sense of place, Paul essentially gives up.