I'm wondering why the German army would write "Germany" in English on their arms
Maybe so that foreign soldiers can return them when they find a lost one.
Almost
It is common practice only on foreign deployments.
Contrary to the US military, we aren't as "arrogant" assuming everyone knows our flag (which is always part of the uniform, home or abroad), hence we put a little "Germany" on it to avoid any confusion.
This is less for the other NATO nations taking part in that misssion who will most likely know the falgs and uniforms of their allies (or they had very bad briefing) but rather for the natives.
Especially in Afghanistan, we Germans like to differenciate ourselves from, say, the US troops. This ususally results in much friendlier behaviour from the locals who, most of the time, aren't too fond of the US... :/
It is also very common to hand our nation's colours on the doors of any vehilcles for the same effect (as big as taking up the whole door).
This is mostly to make sure an enemy RPG soldier won't mistakenly target them from further away...
Whether that always works out or not is another question, though.