To put it shortly but slightly inaccurately, compatibilism basically comes from the idea that "free will" is implied by "moral responsibility", and then it is noted that moral responsibility and determinism are compatible.
> To put it shortly but slightly inaccurately, compatibilism basically comes from the idea that "free will" is implied by "moral responsibility", and then it is noted that moral responsibility and determinism are compatible.
It's actually the other way around: if you acted according to your own free will, then you are morally responsible for your choice.
No, read the link I gave. (Note also that I'm explaining the dominant arguments, not endorsing them.)
If it's still not clear why I put the implication that way around, note that not everyone thinks that you have a moral responsibility in the way Peter Singer argues, but basically every philosopher thinks it's wrong to kick a dog.
I've been studying and debating this issue for years, I know what it means. From your own link, "As a theory-neutral point of departure, then, free will can be defined as the unique ability of persons to exercise control over their conduct in the manner necessary for moral responsibility".
In other words, making a choice of your own free will entails moral responsibility, not the other way around like you said. I don't know what Singer has to do with any of this.
> "As a theory-neutral point of departure, then, free will can be defined as the unique ability of persons to exercise control over their conduct in the manner necessary for moral responsibility"
For more detail, https://plato.stanford.edu/entries/compatibilism/#FreWil.