These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Some readers dislike Augustus for his grandiose mannerisms and his love of metaphor, but others argue that he was meant to be written that way, because wanting to be impressive and memorable is an established character trait of his.
There's also the interpretation that he's mainly interested in getting Hazel into bed. He's a teenaged boy knowing he might die (and for the majority of his time with Hazel knows he's going to die) and he's only pursued girls he knows were dying, suggesting to some that he's not interested in a relationship (and that he perhaps hopes they will be easier to get into bed since they know they won't get too many opportunities to try it). This interpretation seems common among readers who found his courting of Hazel shallow and the relationship itself lacking in depth and being mostly about two hormonal teenagers finding each other attractive. Also there's his comment to Hazel that he hopes bringing her to Amsterdam might get him laid, which some interpret as not actually being in jest. As to why he doesn't dump her once they've done the deed, it can be argued that as his illness progresses he wants to keep her close because she offers him comfort, or that he hopes he will get to sleep with her again.
Some readers also dislike Hazel, feeling that she holds herself to be better than everyone else, is very judgmental, puts down other people's emotions instead of showing empathy and that she is extremely self-entitled.
There are also numerous readers who think Van Houten's behavior is pretty sensible to a reclusive artist whose privacy has been disturbed. He may be a huge jerk, but the points he makes are sound, and his experience makes him unlikely to extend politeness to Hazel and Gus just because they're used to Cancer Perks.
Harsher in Hindsight: In-Universe, Van Houten insults Augustus' intelligence by saying his cancer must have spread to his brain. A Kick the Dog moment on it's own, but then Gus later reveals that his cancer did in fact return and has spread to the rest of his body.
Isaac points out Augustus’s “physical attractiveness” multiple times. Also, Augustus claims that his hot body caused Isaac’s blindness. And on the dubiously canonical Q&A blog that John Green runs (see main page for link), Isaac is referred to as both “gay” and “a [future] ballerina.” Both are said in jest, but still.
Isaac accidentally grabs Augustus’ thigh. The first thing Augustus says to him is, “I’m taken.”
Hype Backlash: After the clip for the “it’s a metaphor” scene was shown at the MTV Movie Awards, it received a surprising level of backlash, due to people seeing it as pretentious when said out loud by an actor.
Plus, what he's describing isn't a metaphor, making him sound like a hipster who's just using random words he heard somewhere to sound smart (which, according to Word of God, is very intentional - Gus is a smart kid, but he uses a lot of words and concepts wrong, like any other teenager).
As seen below, the "pretentious" quote above, combined with the comment John Green made about feminism below, lead to just as much mockery on Tumblr as it's praised.
Iron Woobie: Augustus is this from the start of the novel. He begins to crack by the end.
Jerkass Woobie: Van Houten. Yes, he’s a drunk asshat, but you have to admit he is sort of a tragic character.
Memetic Mutation: This book (not to mention the author) has a pretty big following on Tumblr, mainly for being a massive Tear Jerker and a major source of feels. A common Running Gag is for newtime readers to document their first readthrough of the book and the progressive regression into a blubbering puddle of tears.
“My x are y that I cannot fathom into z.”
“I the way you : slowly, then all at once.”
“It’s a metaphor; you put the x in between the y, but don’t give it the power to z.”
John Green: I just want to point out one thing here: When was the last time the girl kissed the boy in a teen romance? Ever? Has it happened ever? I seriously think it might not have happened ever.note This comment was met with immediate backlash, with people pointing out that this trope is much Older Than They Think. John swiftly corrected himself afterwards, admitting that he got a little carried away with his euphoria over the film being released.
The comment spawned a meme (largely from the book's critics) about John being the inventor of feminism.