It confuses me when people throw a spin on the delivery of
something to overcompensate for the fact that the thing they’re delivering is
unpleasant.
This sentence isn't terribly clear without context. However, I interpret it to mean that people distort bad news in an effort to make it sound better.
This definition for the noun
spin from our dictionary may be helpful:
WordReference Random House Learner's Dictionary of American English © 2023
a particular viewpoint or bias, esp. in the news;
slant: After the presidential debates each side put its favorable spin on the results.
