If you’re an abandoned boy, an orphan almost three times over, you probably don’t see a future for yourself at the Garrison where your family should have been. He knew Adam and Shiro aren’t together anymore, so in his mind, why would Adam want to burdened with another man’s brother?

What’s the best way to solve a problem? Get rid of the source.

Therefore, I believe Keith got himself kicked out on purpose to absolve the one family member he had left of any shame or guilt he thinks he would have caused Adam, which makes the whole thing that much worse. Imagine losing your fiancée and your kid like that. Imagine leaving your father slash brother like that.