EMILY (to Lorelai): That should’ve been you up there. Nothing’s turning out the way it was supposed to.
From the very first episode, it’s been made clear that Richard and Emily are using Rory as a Lorelai substitute, filling up the big gaping hole of their hurt and disappointment with their daughter with hope and pride in their granddaughter.
It now becomes apparent that it hasn’t been possible to suppress and cover up their feelings so easily. Emily has participated in Rory’s coming out as a replacement for the debut Lorelai was supposed to make when she was sixteen – Rory even wears the same dress Lorelai was going to – and yet it hasn’t helped at all, merely brought into sharper focus all that Lorelai (and by extension, her parents) have missed out on in life.
We know that Emily doesn’t believe in arguing or having intense discussions at social events, so for her to fight with Richard in public and make this angry and emotional remark to Lorelai is very out of character. It’s a sign just how frustrated and miserable she’s been.