Could be that we only fast on Asara Beteveis on yom shishi as Rebbi Yochanan himself said by Tisha Beav, אתחלתא דפרעניות עדיף, the start of the punishment is greater. The destruction of the Beis Hamikdash emanated 30 moths later from the siege of Jerusalem. We even would have to fast on shabbos if it could fall on it.
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