Negotiations depend on trust; if there is no respect and trust, there is no way to come to agreement because your word is worthless. And a peace agreement between liars ends in war.
This isn't a stupid game or a reality show; humans will die without an agreed suspension of hostilities. Israel's calculation is that it will kill more than their own will be killed before it will agree to stop seizing other nations' land - it's Putin's gamble in invading Ukraine, it's also why he won't agree to peace talks, for now. Iran knows all of this, they sent professionals. You also NEVER agree to single items without making them dependent on all accepted demands.
Yalie JD Vance isn't even the best liar to send. But his ego is too big to accept he's the sacrificial goat, while UMiami Law School grad Marco Rubio conveniently hides out. Vance is the cannon fodder.