How do I deal with an elderly person's abuse towards me: by remaining silent or by defending myself, knowing that a response is considered disrespectful from their perspective?

The default is that it is permissible to respond to an offender without aggression, but forgiveness and pardoning are better. Allah Almighty says: "The recompense of an evil is an evil like thereof; but whoever forgives and makes reconciliation, his reward is due from Allah. Indeed, He loves not the wrongdoers. And indeed, whosoever helps himself after he has been wronged, for such there is no cause of blame." The desirability of forgiveness and pardoning is further emphasized for an elderly person, especially if they are a teacher; this is because Islamic law encourages honoring the elderly and revering the teacher. A teacher should also be kind to their students and overlook their mistakes.