The English phrase Spit it Out is a command, meaning “say now what you are hesitating to say.”
As you know, spit comes out of mouths and so makes a good metaphor for language. Also, spit it out is what we say to children when they put something in their mouths that they should not eat. So, the phrase implies that it is bad to keep something inside and good to get it out—a common attitude about ideas and emotions in America. Americans value open expression and do not generally consider stoicism a virtue.
We usually say “spit it out” when a person is “beating around the bush”—hesitating to say something straightforwardly. Or when a person is keeping a secret that we want to know!