Some wag came up with the jelly donut jibe well after the speech. “Berliner” was in fact a correct German construct for “citizen of Berlin.” That would be like poking fun at a foreign dignitary who spoke of Manhattan because Manhattan is also a kind of cocktail.
Sure, it was a gibe, we all know what Kennedy meant, and that he was trying to push a sense of solidarity with the people of West Berlin.
Not true at all. If you say: "I am Danish", everyone knows you are a person from Denmark. If you say "I am a Danish", everyone knows that you are calling yourself a sugar coated breakfast roll.
In German, it's even more important to avoid the "ein" in "Ich bin ein Berliner". "Berliner" is indeed, one who was born in Berlin. "Ein Berliner" is just as certainly a Jelly Doughnut. "Ich bin Hamburger" tells us that you were born in Hamburg. "I am a hamburger" says......... Well, you figure it out.