Thug Life was an American hip hop group that consisted of Tupack, Big Syke, etc. They released one album, 1994's Thug Life, Volume I, before disbanding in 1995.
Tupac said, "Thug Life meant 'The Hate U Give Little Infants Fucks Everybody'."
In the novel father asks Starr, "So, what's the hate they're giving the 'little infants' in todays society?" -> They become gang members, because they need money and they don't have a lot of other ways to get it. Corporate America doesn't bring jobs to the Black community. It's easier to find some crack than it is to find a good school. Drugs are a mulitibillion-dollar industry and they are destroying the Black community. People can't get jobs unless they are clean, and they can't pay for rehabilitation unless they get jobs.
That's the hate they are giving the Black community. That's Thug Life.
The first letters of "The Hate u Give" read Thug.