Trying to answer this question has left me with more questions than answers. I'll let the code speak for itself:

type MyAnimals = { name: "dog", fleas: 2 } | { name: "cat" }
function GetKeys<T extends MyAnimals>(animal: T) {
  for (let k in animal) {
    let sansAssertion = k;
    sansAssertion = 'name'; // err -> whyyyyy?
    sansAssertion = 'fleas'; // err -> I get it...
    sansAssertion = 'hohoho'; // err -> yeah, that's Bullsh1t

    const thisIsConst = 'name' as const; // the type is 'name', not string, FOR SURE
    sansAssertion = thisIsConst; // err -> dafuck? Still not?

    let withAssertion = k as keyof T;
    withAssertion = 'name'; // works -> aha!
    withAssertion = 'fleas'; // err -> yeah
    withAssertion = 'hohoho'; // err -> Bullsh1t

    let letsBeExplicit: Extract<keyof T, string> = 'name'; // err -> okay, expected, by now. 
    // Can I assign ANYTHING to this??

    type SpelledOut = Extract<('name' | 'fleas') | 'name', string>
    let noGeneric: SpelledOut = 'name'; // works -> yup, okay, it's not _just_ the Extract that's broken

    type LessSpelledOut = Extract<keyof ({ name: string, fleas: number} | { name: string }), string>;
    let fromKeys: LessSpelledOut = 'name'; // works -> yeees
    fromKeys = 'fleas' // err -> yeees
  }
}

Playground

In case my question isn't clear by now: TypeScript is clearly able to understand the keyof T type and acts as expected. keyof T contains a union of a bunch of different strings (only one, in this case). It would be expected, that Extract<ABunchOfStrings, string> === ABunchOfStrings, yet it is not if ABunchOfStrings comes from a generic type keyof T. Whyyyyy?