Is the speaker considered the cause of death of his brother who drank poison after their quarrel, and was this death destined for him?

You erred in the method of advising; you should have advised your brother with gentleness and kindness. No blood money (diyah) or expiation (kaffarah) is incumbent upon you, because he is the one who killed himself. You should increase your prayers for forgiveness and supplications for him, so that perhaps he may be forgiven, for he committed one of the major sins.