Although I upvote Mark and Alexander, I can suggest an alternative writing trick: Find a way to exchange cause and effect:
You are thinking "betrayal" causes "Kicked Out." Instead think of how "Kicked Out" can be a "betrayal". This is often a puzzler we can't solve, but in this case it is easy:
Your character, out of love for his friend, kicks himself out of the house; and then his refusal to explain why to his friend can become the betrayal.
I'll assume both friends are male; Alex (your character) and Bob (the friend). Alex has no reason to betray Bob, and would never do so intentionally. But unknown to friend Bob, Alex has gotten himself into some trouble (sexual, monetary, criminal) and something happens at the house: If Alex stays in the house with Bob, he now fears Bob is in danger of physical harm, or financial harm, or emotional harm. This could be as simple as Alex getting drunk and having a fling with Bob's ex-wife. Or Alex was embezzling money from his firm and is now concerned he may be caught and Bob would be implicated, if he doesn't clear out. Or perhaps Alex had an indiscreet homosexual affair, and though he knows Bob is not homosexual, Alex fears if Bob is branded as one it will harm his public career (as an actor, politician, whatever).
Obviously I don't know your story or characters, so all of the above may be way off the mark for them. But what you need to invent are non-argument reasons why Alex cannot stay in the house, or Alex thinks it is in Bob's best interest that he (Alex) leaves the house to protect Bob.
That reason should also be something Alex wants to keep a secret because it is embarrassing or illegal.
So the setup is: Alex has decided to kick himself out of the house, out of brotherly love for Bob.
[minor edit here: got my characters confused!]
Now the betrayal: He can't tell Bob why he is doing it. So he tries to make something up instead, but his best friend sees through the lie. It doesn't make sense! Bob says so, Alex changes his story and keeps packing. Another lie! Bob escalates, Alex lies again and Bob becomes angry, Alex doesn't know what to do (he can't tell the truth) so he responds with anger and storms out.
The fight doesn't cause the exit: The exit causes the fight.