Question

Magen David Adom keeps sending me messages all the time saying they need blood to save people, so please come donate.
I heard that rabbis say not to give blood.
But if they themselves needed blood in order to be saved, they wouldn’t say not to take it.
That seems very ugly to me. To take, yes, but to give? To tell people not to give? I’m not a rabbi, but is that really what is written in the Torah commentators?