Pronouns... why the trouble?

"У цьому році я мріяв відсвяткувати 9 травня зі своїм внуком лейтенантом Національної гвардії, але він загинув у бою при захисті своєї Батьківщини", - каже 97-річний ветеран.

Bing translated this as: "This year, I wanted to celebrate may 9 with his grandson, Lieutenant of the National Guard, but he died in battle while defending their homeland," says a 97-year-old veteran. 

 And Google was virtually identical: "This year I wanted to celebrate 9 May with his grandson Lieutenant of the National Guard, but he was killed in battle in defense of their homeland," - says 97-year veteran.

Why do they both just completely miss how to translate свій? WHY? Its very definition is "one's own" - it always goes to the subject of the clause it's in. It cannot be "his" or "their" if the subject is "I' and "he". It exists to eliminate the ambiguity of "John gave Bob his book". Its entire purpose is totally subverted by both these programs. WHY?

MY grandson. HIS homeland.  

So very simple. ... So apparently impossible to derive an algorithm for.

(There are other issues here, like Google's odd punctuation and  the fact that neither one translated мріяв as "dreamed", but let it go, let it go...)