Huh?!
I'm not sure what you find "weird" about the manager being not too thrilled about the idea of your taking a 3 or 4 month leave of absence (paid or unpaid) after you've been there what, 6 or 7 months? In any job it's pretty bad form to make such a request when you're on probation! What did you expect? "There there, you go back to Aussie/Canada/UK and come back when things are settled down and you're good and comfy.."?!
His comments on "We will do our best to make life here as good as it possibly can be, but we are very short staff right now" actually sound sensible to me. And I was reading your post trying to find fault with CX management!
I'm sorry, but I don't know what your point was.