Sadly, like anything good, there's always a catch -- and after Bruce's training is complete and he knows all of the League of Shadows' secrets, he finds himself being asked to execute a man in a show of loyalty.
"Come on, you're embarrassing me in front of my minions. I told them you were cool."
He also is told that Ra's is determined to use Bruce to facilitate the total destruction of Gotham City, something he waited until just now to mention. This doesn't sit well with Bruce, and because he's already balls-deep in the organization, he ends up having to explosion-stab his way out of the League of Shadows, destroying their headquarters in the process.
The best way to show your commitment to not killing your enemies is by blowing them up.
But hey -- free training, right? And now Bruce Wayne gets to be Batman, all thanks to Ra's' total inability to make sure Bruce is cool with murdering people before training him how to bleed out of the shadows and beat the screaming Jesus out of everything on the planet.