Actually sinking a aircraft carrier which houses nuclear weapons warrants a nuclear response, not conventional. Aircraft carrier is appart of triad. You attack nuclear systems you get a plenty of nukes shoved up your ass to put it bluntly.

Iran sinks a aircraft carrier and suddenly your going to have vast sprawling sheets of green irradiated glass across vast areas of the Iranian landscape. This isn't wishful thinking, this is pretty open/public knowledge of the resulting consequences of a nation sinking a aircraft carrier.
Nuclear response does not require being nuked. Simply attacking nuclear triad/response infrastructure can warrant a nuclear attack. Aircraft carriers are a corner stone to the nuclear triad infrastructure.