Why do Paul and kat exchange addresses?

Paul and Kat exchange addresses, so they can meet up after the war.

"Perhaps we could do something together later on, Kat." I am very miserable, it is impossible that Kat--Kat my friend, Kat with the drooping shoulders and the poor, thin moustache, Kat, whom I know as I know no other man, Kat with whom I have shared these years--it is impossible that perhaps I shall not see Kat again.

"In any case give me your address at home, Kat. And here is mine, I will write it down for you."

I write his address in my pocket book. How forlorn I am already, though he still sits here beside me. Couldn't I shoot myself quickly in the foot so as to be able to go with him.