In addition to the other answers, I'd like to mention something that while comparatively minor in impact, is IMO strongest in "there's no plausible innocent explanation for this", which helps to paint a picture of what FTX internal culture must have been like: FTX published on their website how much they had in their insurance fund. This fund was supposed to protect customers from losses e.g. arising from other unrelated customers being unable to pay back their margin loans. The number they published was a complete fabrication, in no way informed by the actual size of the insurance fund (which was typically smaller): it was calculated based on daily trading volume and a random number generator.

There was a bunch of news coverage about this at the time, here is the first result I found on Google.

@Jason left an answer here, referring to this sentencing memo:

I'd look at pp. 5-12 of the linked sentencing memo for customers, pp. 15-18 for investors/lenders for the government's statement of the offense conduct. The jury merely utters guilty / not guilty on each count, it does not provide detailed findings of fact. Judge Kaplan heard all the evidence as he presided at trial, and can rely on his own factual findings at sentencing under a more-likely-than-not standard. Of course, that is just a summary; Ellison alone testified for ~3 days.

Basically, SBF & FTX falsely represented that the customer assets were segregated from FTX's own assets and would not be used by FTX. Yet Alameda regularly took large sums of money out of accounts holding FTX customer funds, and the "allow negative" feature allowed it to borrow ~unlimited money as well. This was not limited to funds made available to customers through the margin lending program. 

At various points discussed on pp. 9-11, SBF directed Alameda to "borrow" more money from FTX despite knowing it was underwater at the time. For instance, at one point SBF directed Ellison “to use FTX customer funds to repay loans" (her words), despite knowing that Alameda was $11B in the hole and was already "borrowing" $13B in customer funds (p. 11). About $4.5B more in customer funds was used to pay Alameda's lenders as a result (p. 11). In short, I don't think the narrative presented in the linked post is backed up by the trial evidence.

(The last sentence in the response refers to this post.)

My understanding is that there are two major claims against FTX:^[1]

Providing a "backdoor" to Alameda Research

1. When you trade derivatives, you can end up with a negative balance. This is not a weird crypto thing but is also true of trading on Fidelity or Vanguard or whatever: you short a stock, that stock goes up, now you owe the exchange money.
2. Alameda research (AR) did a bunch of bad trades, and ended up owing FTX a lot of money. Again, by itself this is not cause for concern. But if you e.g. owe Fidelity too much money then they are going to liquidate your account because they don't trust you to pay it all back. And FTX's official policies said that they would do this, but they didn't.
3. Telling your investors that you will follow a certain risk management policy and then not actually following that policy is fraud. My understanding is that it would have been perfectly legal for FTX to not liquidate AR, it's just the lying about it that is fraudulent.
4. My understanding of SBF's defense here:
   1. The backdoor was created because FTX's code sucked and they were afraid of accidentally liquidating their backstop liquidity provider (AR), not because they actually wanted AR to follow different policies 
   2. And, in fact, AR's net position was positive, it's just that many of the assets weren't kept on FTX itself and were illiquid
   3. So, SBF thought AR was following the risk management policy as published
   4. [The jury did not find this defense persuasive.]

Commingling bank accounts

1. Because FTX was unable to get a bank account, it sometimes told its customers to deposit funds in a bank account that was owned by Alameda
2. Because their code/ops sucked, Alameda thought that some of this money was theirs, not FTX customers', and invested it
3. My impression is that both the prosecution and defense agree that until ~June 2022, this improper usage of funds was due to negligence, not malicious intent 
4. Sometime in 2022, this bug was discovered, and FTX execs realized AR had been investing fiat which wasn't theirs
5. Fortunately, the investments had done reasonably well, and AR had assets which could be converted back into the appropriate amount of fiat, if required^[2]
6. Even though this use of funds was unintentional and sounds extremely sketchy, FTX's general counsel testified that FTX's terms of service did not prohibit it [though maybe it was implicitly prohibited, see this comment]
7. However, the prosecution pointed to statements that SBF made to the public which seemed to portray this type of action as prohibited, and the jury found this persuasive
8. Again, my understanding is that FTX's actions here per se were not criminal, the crime came because they lied about what they were doing. If SBF had just not made public statements beyond "read the terms of service", there would be no fraud. [Edit: this is disputed, see here.]

A final point: SBF's defense relied almost entirely on "good faith", i.e. claims that FTX's risk management systems were so terrible that he wasn't even aware that his behavior was fraudulent. And the prosecution even agrees with this defense at some points. Since your question was about what FTX did wrong, consider that FTX's poor risk management should reflect negatively on them, even if it doesn't qualify as criminal behavior on behalf of any individual.

1. ^{^}

   This comes mostly from the closing arguments. Note that actually most of the arguments were the prosecution and defense trying to convince the jury that SBF is a bad/good person respectively, and not actually engaging with the concrete details of what happened. So I'm trying to summarize what seems to me to be the most relevant part, but I expect I'm getting things wrong, and would appreciate corrections.

2. ^{^}

   At least under certain valuations of the assets. My impression is that these valuations were not done rigorously, but their accuracy is not that relevant to the criminal charges against SBF.

The FTX estate (which I understand includes Alameda) did a lot of things wrong, but regarding this:

What made the lending out to Alameda fraudulent?

FTX promised many times, in many different forums, that it had sophisticated risk controls that would automatically liquidate customer accounts when limits were breached. Then it turned out that this was true for most counterparties, but Alameda was a big multi-billion dollar exception.

I think there’s an argument that if FTX had kept its promises about risk controls, there wouldn’t have been a criminal conviction, though possibly that would have negatively affected the business in other ways.

I don't have a link on hand but Matt Levine has some great articles explaining the collapse of FTX. Perhaps check out some of the stuff he wrote in November 2022 when the news was just breaking for background & then more recent stuff for a fuller picture. :)

I also initially misinterpreted the title so maybe consider renaming it something like "Can someone explain the FTX fraud?"