Overuse of possessive adjectives (my/your/our/etc.)

Sorry, misprint: agree with Jim

I have to say I don't understand why speakers of other languages seem to think English is illogical in this respect. I didn't realise it was the only Indo-European language to use the possesive in this way, although having learnt German I knew this particular language didn't use the possesive in this sense i.e. ich buerste mir die Zaehne and not meine Zaehne. But of course there is then the reflexive involved,the 'mir' shows that you are referring to yourself. Why in English would we not wish to indicate that we are referring to a part of our own body, as opposed to some body part in general?

i'm not saying it struck me as illogical; it struk me as excessive: he closed HIS eyes; he pulled his hands from his pocket ,etc.
You can see things like these only through a comparison, not just being inside your mother tongue.