Sorry for the battering of rhetorical questions, but...
...what is "to be proud of a country"?
Achievements of people from the past? But you see people with laudable achievements through the whole world. Why specifically those associated with your country, instead of, say, another? And more importantly, why aren't we proud of what we, as individuals, do with our present?
Proud of a culture? I get that people relate to others sharing their culture; but contrariwise to what that Napoleonic meme says (with all its disgusting implications), countries don't need to coincide with cultures. Cue to Switzerland, a clusterfuck since HRE times, faring far better than a Portugal who has been culturally homogeneous since 1100.
And even demarcating cultures, gets tricky and arbitrary. It's all a bunch of continua. Eventually this sort of proudness will boil down to "I'm drawing the line HERE. This one is from this side of the line, so I'm proud of them. That one isn't, so who cares."
Is it being proud of your impact on others, through your everyday interactions? But most people in a country - even a small one (more like Andorra than Denmark) - are not meaningfully affected by you.
So, to keep it short: every single thing that we could be proud of, as human beings, is better serviced by either a smaller or bigger identity.