Alas, there was no supereruption/
In the long chrono (17th c BC eruption hypothesis) the Minoans continued as if nothing happened for almost 200 years. That idea is, of course, makes nonsense of the impact of the eruption, but is consistent with the fact that there wasn’t one.
In the short chrono (15th or 16th c BC eruption hypothesis) the Minoans continued as if nothing happened for almost 100 years. That idea is, of course, makes nonsense of the impact of the eruption, but is consistent with the fact that there wasn’t one.
There is no evidence of a tsunami, by which I mean, there’s no remains of any large and higher-altitude debris line, anywhere in the Aegean basin. That’s difficult to reconcile (ahem) with such a large event, but is consistent with the fact that there wasn’t one.
Minoans were in Egypt during the 18th dynasty, but that dynasty wasn’t anywhere near as long ago as the 17th c BC (Amarna was actually late 9th c BC; the conventional pseudochronology is way off).
I was researching another question and came across this article. It lists measurements of ash fall in various areas around the Mediterranean and in ice cores. I get the impression that most feel this evidence indicates a major eruption.