People are arguing Buttigieg dropped out because he is otherwise unemployed and hopes to earn "good guy" points toward a job in a New Democratic administration. I don't buy it; evidence suggests that, in spite of his hyper-curated public image, he is seriously smart.
The likelihood of a Democrat occupying the Oval Office in January, 2021, isn't terribly high and I'm fairly certain Pete knows it. He probably knew it before he started.
Buttigieg won one state and some delegates, got his name into the public consciousness, and bailed out before he embarrassed himself with poor showings in too many minority-heavy states. This is excellent window-dressing for later, maybe for 2024.
If we get a black swan event and a Democrat is elected this fall, Buttigieg probably wouldn't turn down an offered cabinet post. But I don't believe his hopes are (or should be) high.