Is refraining from greeting someone to avoid their ill speech, after a previous quarrel, considered a severance of ties?

Not greeting your brother is a forbidden form of severance, for the Prophet, peace and blessings be upon him, said: "It is not lawful for a Muslim to abandon his brother for more than three nights. They meet, and this one turns away, and that one turns away. The better of them is the one who initiates the greeting of peace." So, hasten to give the greeting of peace to attain the reward. If your greeting is returned, you both share in the reward, but if it is not returned, then he has incurred sin. Respond to ill-treatment with good, as Allah Almighty said: "And not equal are the good deed and the bad. Repel [evil] with that which is better; then suddenly he to whom between you and him was enmity [will become] as though he was a devoted friend. But none is granted it except those who are patient, and none is granted it except one having a great portion [of good]."