What does it mean if a professor asks you to draft his reference letter for you?
For me, it means two things:


I am really busy
I don't know anything about the job you're applying to and what you want to emphasize about yourself


If the first draft you write is something I can't sign, I'll edit it or I won't sign it. If it's not braggy enough, I might add some emphasis. But metaphorically handing me a piece of blank paper and asking me to recommend you is actually asking me to put in quite a lot of work. Do these people you're applying to value initiative? Creativity? Willingness to work long hard hours? Cheerfullness? A driven nature? A gentle spirit? Is the fact you write great software relevant to them? How about your careful bench work? For all I know you want to do less of one thing and more of another. So now I need to ask you a zillion questions about what you want to emphasize, and maybe go research the job too, and then ask you if what I've written is ok - frankly, it's way easier to ask you to write the first draft. And some days, I take the easy route.

It does not mean:


I intend to sign words I didn't write. I will write the final draft
It's ok for you to make up strengths you don't have
You'll know what I send in the end
I can't write a simple letter without help from a student.


Your first draft doesn't even have to be a letter, it can be point form. But tell me you're choosing me as a reference so I can confirm your amazing Xness, Yabilty and Zation. If I can, I will.

By the way, I wish I could find the idiot who started the theory that it means I don't think well of you and want you to retract your request. Several students have retracted their requests after I asked for a first draft, and that's a shame, because I would have cheerfully signed a glowing recommendation for them. I just didn't have time to write it all from scratch myself.