The first step that Jethro takes in growing up is the little crust of bread dipped in coffee by Bill. Coffee is considered "an adult luxury" (1.95), so Jethro partaking in it symbolizes a baby step in his departure from adolescence and arrival into adulthood. We're not equating the coffee-soaked crust with a coming-of-age welcoming parade for Jethro, but instead just saying that it's a small step in the right direction for young Jeth. Jethro's definitely still a kid, which we're reminded of when Bill slabs some butter on to make it all not taste so bad.
Which brings us to our next point: a steaming cup of black coffee tastes nothing like the "venti soy caramel macchiato with mocha, espresso, and skim whip" that Starbucks offers. Depending on the roast, a good cup o' pure java can have slight variations from fruity to earthy to chocolaty (definitely our favorite)—but the first word that pops into people's mind when they think black coffee is usually bitter. Kind of like adulthood, which Jethro definitely gets a bitter taste of thanks to the Civil War.
The second time Jethro tastes coffee is before he heads off to Newton to pick up some more coffee for his ma. Before setting out, Ellen "made [Jethro] share her coffee that morning, a fragrant cup diluted with hot milk" (5.27). It's more of a taste than he gets from Bill's bread crust, but is also still diluted which lets us know that while Jethro has come into his own a bit more, he is still a kid facing very adult circumstances.
Speaking of adult circumstances, it's on this trip to pick up coffee that Jethro finds himself on the receiving end of a whole lotta Guy Wortman. It's no surprise that Jethro includes this event in what he considers to be "a time when he left childhood behind him" (6.16)—it's a pretty scary interaction, and the threat of violence is very real. In other words, it's got adult written all over it. And to think, all of this went down because of a little bit of coffee.