Of course every politician is going to say that the country they lead (or are trying to lead) is the best country on Earth. Who wants someone to run their country who doesn't believe that (or at least pretend to)? You want the person running your country to be proud of it and most people have some sort of national pride that that statement appeals to.
As for actually backing up the statement, well, you can look at studies and surveys relating to happiness, quality of life, crime rates, etc. and see the same 10 or so countries on the top of each of those lists. But those criteria might not be everyone's definition of what makes a country the best country, so yes, it's highly subjective. I live in Canada and while I am definitely proud of my country and think it's ONE of the best, I don't think I could say it's THE best. For me that would probably be one of the Scandinavian countries. But, again, my criteria is probably much different than someone else's. There are lots of people who whole-heartedly believe that the US is the best country in the world and I wouldn't live there if you paid me to. Different strokes for different folks!