Yep, the recycling/trash system is nightmarish. Furnishing a new apartment (they don't typically come with anything, including a washer or fridge) results in a huge amount of packaging (the Japanese absolutely love to box, rebox, bag, rebag, wrap, rewrap, etc.) which makes your first month a very nasty lesson in how trash pickup works and doesn't.
On the same logic moving out of a place requires planning in advance what to throw and when. You're moving on saturday and have to throw your remaining cleaning stuff ? Too bad, non burning garbage is on tuesday. If your building doesn't have a garbage room you'll be pissing off the neighbourhood for 4 days.
I was going to justify all the complexity by an extremely good recycling rate, but it seems Japan is at 20% on average, which is behind 16 other countries [0], way behind South Korea.
If you are moving out, then you bring the trash of the old apartment with you and you throw it the day that you are supposed to throw it in the new neighborhood.
It is a no-brainer for Japanese.
Been there, seen that. :)