I'm confused. This is notice from the FDA that the additive will no longer be permitted. It then goes on to explain why it's perfectly fine to permit it....

The petition requested the agency review whether the Delaney Clause applied and cited, among other data and information, two studies that showed cancer in laboratory male rats exposed to high levels of FD&C Red No. 3 due to a rat specific hormonal mechanism. The way that FD&C Red No. 3 causes cancer in male rats does not occur in humans. Relevant exposure levels to FD&C Red No. 3 for humans are typically much lower than those that cause the effects shown in male rats. Studies in other animals and in humans did not show these effects; claims that the use of FD&C Red No. 3 in food and in ingested drugs puts people at risk are not supported by the available scientific information.

This is what we've decided to do and this is why that decision doesn't make any sense. More at 11.

[–] millie 2 points 13 hours ago

The explanation is literally the sentence after you stopped quoting.

The Delaney Clause, enacted in 1960 as part of the Color Additives Amendment to the FD&C Act, prohibits FDA authorization of a food additive or color additive if it has been found to induce cancer in humans or animals.

They're prohibited from authorizing it as per the Delaney Clause because it causes cancer in rats. The FDA doesn't get to make decisions unilaterally, they have to follow guidelines. Because their guidelines say that color additives can't be authorized if they induce cancer in animals, they can no longer authorize the additive.