Asoro b'Teves is the only fast that even if it happens to fall on Shabbos, we'd have to abstain from the beer and Cholent. That would be a crisis, which the Rabbis saw in their ruach hakodesh would be untenable, so they preset the calendar so that it never falls on a Shabbos.
In what way is asara b'teves different to all others?
On this day we recall the first opening steps which began the destruction of G-d's home on the Temple Mount. The Jewish people were still going strong, but, since it's the beginning, it's the most significant
What's the lesson for us?
The beginning is the most significant.
I found for myself that jumping on the Chart was the challenge, and plenty good came from there. I have other struggles which I need to begin small steps to, be'H.