I'm going to drop a friend in their time of need
Why would you do that at a time like that?
He has been dismissing me since then, even though I've lost my father.
They need to get over their issue, and might need your help. You shouldn't cut them out of your life at a moment like that.
They abandoned me, so I will do the same to them.
You shouldn't do that. If you stayed friends with them, then you must have valued your relationship with them despite them abandoning you before. Don't let petty revenge sour that relationship.