Is that new?

Once someone has replied you cant delete.

I assume you mean used the quote feature.

Thread you start - you can no longer delete it, once someone has made a reply to it.

Post you start - the Delete feature is still there, if you want to delete that post of yours.

As stated, the original post in a thread cannot be deleted once there is a reply—and no, not just a quote: any reply.
I just killed (deleted) a thread I started, but that was possible only because no one had posted a reply.

You can, however, delete the contents of an initial post or edit it to something like a single period (.), including the subject line. Whether that would be appropriate in view of what's posted in follow-up replies would be something to consider.

As a bit of history that some here may remember, long ago it was possible to delete the initial post in a thread one started, and that then would delete the entire thread including all replies by everyone who posted in the thread. That was later changed to the current situation.