Edit: and the contrary is true, Americans loves their army, and they are all about that "thank you for your service" rhetoric, so perhaps just Israel top that.
Also Switzerland has conscription / compulsory draft, and among a lot of Swiss, the army is seen with sympathy.
That said, I met a couple of Israelis that left the country for good because their experience with the army was so bad. I guess that there is some "voting with legs" going on.
I think spending part of your young adult life participating in the actions and socialisation of an institution, and then living in a society where everyone around you shares that experience, creates far stronger emotional influence on people's judgements than seeing some people you don't know being shot in a far away country.