Lethargic Man (anag.)

I think, I compared Tisha BeAv and Purim, because I tend to focus at Tisha BeAv more on the human catastrophe then on the temple. When I hear Eicha, I think about the countless people who suffered then - and in later centuries, as we are reminded in the kinnot. So there is this interpretation of the Purim story, that although God is not mentioned, He was present and prevented the worst from happening. But why then and not later? Therefore, I think, both days raise the questions, whether one can believe in a God, who has influence on human history.

Good point. Though for (almost) all premoderns, along with a substantial number of the Orthodox to this day, the explanation for the Destruction of the First Temple is that given in the Book of Kings: that it was in punishment for the people's idolatry; and that for the Second was because of שִׂנַת חִנָם—causeless hatred (which latter you don't need to be a literalist to accept as the cause).

I'd like to know, what parallels you would draw between Purim and Yom Kippur. Similar sounding name, calendrical opposite, this doesn't sound like a big connection. I also can't think of anything in common between these days.

Well, I wouldn't draw the connection, but others have (http://www.ou.org/holidays/purim/every_day_purim_every_night_kippurim).