He refers to the context as justification for switching the verbs. However, Jesus does not always reply directly to a specific question asked of him. Especially to those whom he knows are only seeking to trap him and give reason to kill him.Wait a minute. Not to defend your opponent here —far from it!— but what do you mean, "("To become" can simply be replaced with "was" with no loss of meaning.)" ? Do you mean that the two translations are equally valid use of the originals, or do you mean that the two English renditions are the same in meaning? They do NOT mean the same thing.
Jesus might just have easily passed over their question of seeing Abraham and been making further reference to Abraham’s ardent desire to see Jesus’ day.(v 56) Which he will, at the resurrection of the dead.
As Abraham believed Isaac would be raised from the dead.