Powerful, angry blasts come out pretty quickly. "You're raping my childhood!" is among the most incendiary statements I can recall seeing regularly with regards to a reboot, as if remaking a film voids the existence of the original (and the memories associated with it, which is actually what your childhood is made of... not the movie itself.) But even without reaching hyperbole, continuations of any kind that weren't part of the original plan (a la a trilogy) tend to get ripped a new one.
Sequels probably get the least frustration, as it is a continuation of the story. Spin-offs tend to be relatively safe as well. Continuing the story in a linear fashion is the safest way you can continue a story, and sometimes people even like it. Even when franchises get renewed when each installment is progressively worse (I'm looking at you, Transformers and Teenage Mutant Ninja Turtles) the anger doesn't seem to get directed here, just generally apathy and the slow descent into being a cultural punchline.
Once upon a time I thought Prequels were the most hated version of re-iteration, and maybe they were, but they're not anymore. Something about continuing a story that seemed complete by going before the beginning and providing more context and narrative before the cameras originally started rolling was seen as... revisionist, perhaps. It doesn't help, I think, that some notable prequels have been pretty rough (but have definitely gotten a harsher public treatment for it than my above references, which just continued the story.) I'm thinking specifically of Episodes I-III of Star Wars and The Hobbit Trilogy.
So on to the worst of the worst, the most wretched hive of scum and villainy - reboots and remakes. I'm not honestly sure what the semantic difference is; a reboot is a remake with intentional differences? Any remake without differences is just a rhetorical exercise in "look how much effects have improved since last time," so let's treat them as the same.
A lot of the hate comes from the perceived pollution of the beloved. If you loved Robocop, you probably weren't all that excited about the Robocop reboot. The idea is that by making it again, it ruins the first, and I'm not sure I buy into it. It's the most emotional of critiques, rooted in nostalgia, and nostalgia is a really dangerous and particularly useless metric by which to evaluate something. Good remakes seem to be quickly forgotten (at least the fact that they're reboots); I'm looking at you, Mad Max: Fury Road. Is there a timer somewhere, for how long it needs to be before you can try it again? How much of the original team needs to be involved for it to be ordained?
I recently saw someone say, regarding a film that was being rebooted "I'm so pissed 1) that they made this and 2) that they spent however much money to make it!" It really narrowed to a point to me why I don't understand the collective frustration. Making a thing doesn't take away from you, or from the thing, in any meaningful way. Entertainment is voluntary participation only, kids. And that money, regardless of how much it is, was going to be spent on making a movie, not financing breast cancer screenings or feeding inner city school kids- making movies is what the entertainment industry does, so the better question is Why This Thing?
And finally we get to the creamy, delicious, nougat-y center of the public social media outrage.
It's your fault.
People have been complaining that Hollywood only makes reboots and remakes and sequels for as long as I can remember, so we're talking at least twenty years, and I doubt it was new before that. So if they're still redoing it, there's gotta be a reason, and sheer lack of originality ain't it. It's a cheap reason to lean against while we shake our fists and complain, but that's like telling the first wave of classic film makers that they're shitty storytellers because they made Dracula or Frankenstein or MacBeth.
The real reason it happens is because we go. We buy a ticket. We sit and watch. Whether it's to be vindicated in our anger, or in cautious optimism that it might be good, or to relive just a tiny shred of that nostalgia we so rabidly seek to protect, we're going and watching. Franchises (even bad ones) are remarkably good at putting butts in the seats, way more than new films. A franchise is brand identity in the same way your favorite restaurant has brand identity, far more than the production house itself (or nearly anyone involved, except the starring actors, who's brand identity is a whole other source of frustration.) The value of that brand identity is significant, and if you're at all familiar with business, then you're aware that it's much, much, much more expensive to make a new customer than it is to retain an old one.
In essence, it's a lot easier to sell you the likely-terrible Fast and The Furious Sixteen: More Wheels than Weal than it is to get you to see the unknown vector Tomorrowland. And that's not just based on economic philosophy, but on market data and research that's huge and deep and would probably constitute quite the fire hazard if you ever printed it all out at once.
At it's core, the argument against Reboots & Friends is about as strong as saying "I hate those dirty burger flippers" as you drive away from golden arches with fifty bucks worth of fast food. If we (as both individuals and the larger buying public) demonize the thing at the same time we patronize it, the argument is fundamentally undermined. We can't actually send the message of "try harder to make good, new content" or "don't beat a good franchise to death" if we line up to watch them beat the dead horse like an old rug.
I'm sure there's more to say about this, but my train of thought has completely run out of steam, so I'm going to leave it here. Maybe I'll pick it up another time.