Well, Olaf is in kind of a identity crisis. Let me explain.
You see, when the whole Class/Subclass thing started back in 2016 or so, Olaf was first listed with the Juggernauts.
Juggernauts are champions like 
and 
and 
and 
and so on.
They are described as the following: Juggernauts are melee titans who relentlessly march down the opposition and devastate those foolish enough to get within their grasp. They are the only subclass who excel at both dealing and taking significant amounts of damage, but in turn they have a tough time closing in on targets due to their low range and extremely limited mobility.
Olaf USED to be listed among the champions in this subclass. BUT, when they did a second pass about a year later in 2017, Olaf was placed among the Divers. The reasoning for this? You got me. (Of Course, Skarner was originally supposed to be a Juggernaut, as we all recall his whole inclusion in the inaugural Juggernaut Update, but that's a mess all its own)
So I think with the way his kit is currently set up, he can't be nailed down reliably as one type or another. Let's look at it.
Passive: AS (Attack Speed)% increases as Health% gets lower.
The passive grants him more AS which means he has access to continuous damage or DPS. Makes sense since like ADCs, Fighters are supposed to be DPS-based. That applies to both Divers AND Juggernauts.
Q: Skillshot based Axe-throw that damages and applies a slow only if the skillshot connects.
This is both a damage skill and provides Olaf with his main form of CC. This is something that could place him more in the Juggernaut-area, as he has only 1 form of CC, this slow on the Axe.
W: More AS, as well as Life-Steal AND increased healing from all sources based on his missing health.
This is something that's a little confusing, at least IMO. He gets AS (Somewhat like Jarvan's flag or Xin's dash do) for activating it, on top of any AS he already has from his passive, so that COULD be a point for the argument that he's in the Diver class (As most Juggernauts usually don't have anything that grants them instant AS boosts aside from maybe Urgot's W, and even then he attacks at a FIXED AS rate while it's active rather than boosting his existing AS). But, this also grants him Lifesteal AND increased healing and while sustain via in-combat heals is something SOME Divers have (Like 
or 
), sustain via in-combat heals is USUALLY attributed more to Juggernauts (Such as Q heal with Outer Circle of Q, or 
heal on Q, and so on). So this has arguments for BOTH classes, as the free AS leans in the Diver direction, while the Sustain leans in the Juggernaut direction.
E: Deal true damage to the target.
This has some aspects of both Divers and Juggernauts AGAIN. It deals true damage, something often seen in Juggernaut kits ( Dunk, Villain passive) and acts as a Auto-Attack Reset, if I'm not mistaken (Haven't played Olaf in a long time, so correct me if I'm wrong) which is something else that Juggernauts often have. But the cool-down for the skill is reduced by Auto-Attacking, something NOT seen in Juggernaut kits IIRC. That points again back in the Diver direction.
R: Passively grants resistances when not active. Removes CC and becomes immune to any following CC after activation as well as bonus AD. Grants Movement Speed for 1 Second in the direction of nearby enemy champs.
This skill is a mess all its own. First, he is granted FREE resistances (Granted it's a flat amount, but the point nonetheless stands) for not using the skill. The only Juggernauts with comparable things are Nasus, Trundle or Shyvana. (
gets his from his ult, as does 
while 
gets it on her main passive, and even then, Nasus and Trundle's boosts are only temporary, while Shyvana's only increases if she can kill Epic Monsters like the Dragon). No other Diver has FREE Resistances for simply existing. And the Juggernauts that have it ONLY have it temporarily with the exception of Shyvana, and even then hers is minuscule (A whopping 5 of each) and ONLY increases IF she can kill Dragons.
He also gets free AD JUST for using it! Sure, gets free AD, but he HAS to activate Noxian Might first and that requires all 5 stacks of his passive on a target or killing someone with his Dunk. So that could be a Juggernaut point again. BUT, Olaf ALSO gets FREE MOVEMENT SPEED just for activating it! This skill is ALL OVER THE PLACE! Let's JUST list what THIS SKILL ALONE gives.
Free Resistances- Would be more in line with Tanks like Vanguards and Wardens.
Free AD and CC Resistance/Immunity- In line with Juggernauts.
Free Movement Speed: In line with Divers to try and get on backlines.
So I hope this exemplifies just what a big heaping mess of ALL SORTS OF CLASSES AT ONCE, that Olaf is. Sure, he has more Juggernaut traits than Diver, but he's got more Diver traits than he has Tank/Vanguard or Warden, so, really, where DO YOU put him? I'm kind of surprised that HE didn't end up as one of the choices on that 2020 VGU vote.
