Because people hate change.
Let's look at what changed and didn't change with DmC, shall we.
DmC failed to change so much that actually matters: Progression is still completely linear since the mission/chapter system still sticks to the series like gum in its hair, the enemies are still slow and unreactive punching bags with two moves max, bosses are still mostly slow hulking dullards that lack the appropriate tools to challenge the player (like no goddamn anti-air attacks. For examples of how big hulking bosses should be, look at Ludwig and Darkbeast Paarl from Bloodborne), instead of getting rid of the pointless platforming they doubled down on it, the weapon/style switching is still unnecessarily convoluted, they failed to shake up the level design, the art design doesn't amount to more than pretty scenery instead of actually interesting locations (look at Dark Souls and Bloodborne. That's what DMC should aspire to, instead of dull gray-ish cities and pretty skyboxes), they made the "area closes off" scripted events before battles even more fucking annoying, no Boss Rush Mode, no co-op, no NG-esque mission mode, it continued a proud series tradition of getting rid of a bunch of great features from previous games (this time no Royal Guard, no Air Trick, no Sword Pierce/Dance Macabre, no Twosome Time, no Gunstinger, no DT-exclusive moves, no Distortion, no Inertia or Guard Flying, no Nero or any of his mechanics; still no crazy combos, Free Ride, Pole Swing, elemental weapons, obtaining bosses as weapons, Quicksilver or unique firearms like Artemis or Spiral). I could go on and on and on.
As for what they actually changed: The story is a retread of DMC1 and DMC3, the concept of Limbo has little impact on gameplay, the urban environments meets demonic wonderland amount to pretty looking skyboxes instead of actually interesting level design, modern trends like cinematic set pieces and forced walking sections, boss fights are interrupted by cutscenes and scripted events, they got rid of the lock-on which fundamentally changes the combat system and breaks the combat on higher difficulties, the launcher is now on a dedicated button with only two possible functions, more gosh darn bush-snorting stick-licking platforming, zero gravity on aerial moves meaning air combat is dead simple, the Angel/Devil system restricts the freedom of the combat needlessly, the weapon switching is even more convoluted by combining a toggle based weapon switch with the weapon switching of DMC3
and the stupid weapon shuffling from DMC4, weapons are now light/medium/heavy which sucks the fun out of combat even further, the combat has less options because of a more limited move set even though there's two more weapons than DMC4, Dante's Devil Trigger is the worst version yet as it offers nothing beyond an anti-grav feature and a generic power up, and again it got rid and ignored of a bunch of great features from previous games.
Gee, I wonder why DmC's changes were so negatively received. Thankfully the game actually did a lot of cool stuff, most of which gets ignored by most of its supposed fans and its detractors.
As for DmC Dante, no, people didn't hate him because they "hate change". They hated DmC Dante because the initial reveal was absolutely terrible, because instead of taking the criticism to heart Tameem and Capcom's Alex Jones dismissed fan concerns and insulted them. They hated DmC Dante because he's much less of the goofy cartoon character that people loved. They hate DmC Dante because he fucks strippers in the intro, and lives in a trailer. They hate DmC Dante because he dresses like a hobo. They hate DmC Dante because of the nature of the reboot his character represented a regression of all the development the original version of the character had undergone.
You can argue that some or none of those things matter. Personally, I don't really care about the changes that much because gameplay is no. 1 to me. But no one hates DmC Dante solely because they "hate change". It's a completely embarrassing notion and something that sounds like drive-by YouTube comment rather than a NeoGAF post.
I'm sick to death of every DmC related thread being the same garbage ad nauseum. Random DmC stans insulting fans over trivial bullshit while ignoring the actual interesting stuff the game did because their interest in DmC will never be anything but shallow gravy, while on the other hand a bunch of DMC weekend warriors shout about how DmC was the worst thing ever and worse than DMC2 and while also failing to acknowledge the before-mentioned great additions to the formula that DmC had.
We're so goddamn lucky that people like Rahni Tucker and NeoGAF's own TribladeX were involved in DmC because I shudder to think about what kind of shit fest DmC would have been otherwise.
Edit: Just so people don't gloss over it because it was a response to an unrelated comment, cool things DmC actually introduced which would be very, very, very welcome in any future DMC game:
Fully 360 degree rotatable camera system, full 360 degree maneuverability in mid-air instead of the forced jump arcs of previous games, Ricoshot, Reverse Rainstorm, Aquila's mechanics, the changes to Vergil's combat mechanics and move set, Dojo/Training Mode, extensive stat tracking found in the options, in-game speed increasing by 10% at S rank and above, the changes to the upgrade system such as upgrades costing 1 point and upgrade points being tied to the style meter, the ability to try out moves before buying them, generally more intuitive menu system/interface, being able to quit and continue from the last checkpoint, secret missions being available from the menu, features like Turbo and Super Mode being toggles in the main menu instead of hidden in the options, almost no forced backtracking or puzzle solving, bosses get their own separate missions, environmental hazards which are useful in combat, enemies that can parry attacks mid-air/mid-combo, unique enemy types like Tyrant (large hulking enemy) and Witch (support-type long-range enemy), charge moves charge faster and are therefore much more useful, pause combo-switching (i.e. continuing a pause combo with a different weapon) which is accompanied by a controller rumble and a flashing of the weapon, pause combo-switching for aerial combos, moves with just frame properties for all weapon types and not just gauntlets, improved style visual UI as Style rank up is indicated by the letter filling up, the style ranking system in DmC DE which is the best version of any game in the series, toggle-based lock-on, Bloody Palace timer option, Must Style Mode, Gods Must Die as an official feature.
The best things DmC gave us were a fully 360 degree rotatable camera system, full 360 degree maneuverability in mid-air instead of the forced jump arcs of previous games, Ricoshot, Reverse Rainstorm, Aquila's mechanics, the changes to Vergil's combat mechanics and move set, Dojo/Training Mode, extensive stat tracking found in the options, in-game speed increasing by 10% at S rank and above, the changes to the upgrade system such as upgrades costing 1 point and upgrade points being tied to the style meter, the ability to try out moves before buying them, generally more intuitive menu system/interface, being able to quit and continue from the last checkpoint, secret missions being available from the menu, features like Turbo and Super Mode being toggles in the main menu instead of hidden in the options, almost no forced backtracking or puzzle solving, bosses get their own separate missions, environmental hazards which are useful in combat, enemies that can parry attacks mid-air/mid-combo, unique enemy types like Tyrant (large hulking enemy) and Witch (support-type long-range enemy), charge moves charge faster and are therefore much more useful, pause combo-switching (i.e. continuing a pause combo with a different weapon) which is accompanied by a controller rumble and a flashing of the weapon, pause combo-switching for aerial combos, moves with just frame properties for all weapon types and not just gauntlets, improved style visual UI as Style rank up is indicated by the letter filling up, the style ranking system in DmC DE which is the best version of any game in the series, toggle-based lock-on, Bloody Palace timer option, Must Style Mode, Gods Must Die as an official feature.
If anything it shows that they don't understand writing themselves. Because they're taking a scene that most definitely isn't taking itself seriously as a completely straight faced attempt at being edgy when it's the opposite.
You're ignoring context. Merely an hour before we have a scene where Kat explains in dead pan about how she was abused and raped by her step father who was a demon. The tone of DmC, like the originals, is all over the place.
If people misunderstood anything about the story, the game itself is to blame.