Step 0: Citadel pays Robinhood for order flow. Citadel gets to see RH's orders a few milliseconds before they're filled. Citadel may choose to front-run some of those trades.

Step 1: RH's customers and WallStreetBets start manipulating $GME. This is happening in the open.
Officially, they're manipulating $GME (and $BB and $KOSS) because these low-value stocks are being very heavily shorted, and if something moves the value of the stock up (like, tens of thousands of retail investors acting in near unison), those short-sellers may be forced to sell
...to cover their borrowed shares. [Ed. note, this is a typo he corrects further down. He meant to say "buy to cover"] If most shares are held by retail investors who won't sell, the price will skyrocket (supply/demand) until someone does. The bear hedge funds and such will still have to buy to cover, which may cause a bit of a liquidity crisis for the funds.
The concept of "Screw the hedge fund vampires who exist only to destroy companies like Gamestop" is a big part of /r/WallStreetBets's messaging. It's a compelling message, and a decent secondary reason for this.

The primary reason to manipulate markets remains profit, though.
Step 2: HFTs buy shares ahead of Robinhood users.

Remember Citadel, the firm who can front-run robinhood trades, and got to see all of that RH data a little early because they paid for flow? Yeah. When do you think they started buying $GME in front of RH traders on momentum?
Because the volume of shares exchanged suggests that the HFT folks were all over this, all the way to $150. The message on WSB might be "lots of little guys screwing big Wall Street", but the truth is that the HFT robots were screwing everyone, while paying RobinHood a kickback.
Step 3: A hedge fund becomes insolvent. Today it was Melvin Capital Management. It very likely won't be the last.

Melvin immediately sells off a portion of itself, because it needs the influx of cash or it will vanish in a poof of smoke, vaporizing ~$15 Billion in the process.
Step 4: Who's the lead investor, picking up part of a usually successful fund at fire-sale prices?

Right. Citadel, probably with some of the cash they made by repeatedly profiting in the milliseconds before filling the trades that collapsed this fund.

WSJ News Exclusive | Citadel, Point72 to Invest $2.75 Billion Into Melvin Capital Management
Hedge fund Melvin Capital has been hit hard by a series of short bets to start the year, down nearly 30% for 2021 through Friday, people familiar with the firm said.
https://www.wsj.com/articles/citadel-point72-to-invest-2-75-billion-into-melvin-capital-management-11611604340
Step 5: Citadel still has access to RH order flows, is still allowed to front-run them and/or pocket the spread, and can use that and other information to determine the next over-leveraged fund that's going to get squeezed.

They might even be able to accelerate the squeeze.
So, the next time you discount the impact of "4chan with a bloomberg terminal", remember that they are not the only ones who stand to benefit from intentionally screwing exposed short-sellers.

The professionals are all too happy to amplify the efforts of the amateurs for profit.
Because if amateurs manipulate the market, uh, truthfully, then nobody loses their license.

"I (retail investor) bought because I hate Citron & hedge funds, and we're going to screw them for profit. Join us, but do your own due diligence. YOLO!" might just be legal. IANAL.
If a licensed broker/dealer did this, they'd lose their license, and probably go to jail. Martha Stewart did time for less.

But Citadel, by paying for order flow and sitting in the middle, gets to legally ride-along, printing money the whole way.
So, when you ask yourself, "who pays for no-commission trades, and why?" or "what's the harm of RobinHood's business model?", take a look at what happens behind the scenes, in the milliseconds after you press buy, but before you own those shares.

It's vampires all the way down.

buy. buy to cover. My kingdom for an edit button.