Having an institution named the United Nations does not, in itself, create unity among nations. Whether it does or not is something that can be judged after the fact or, if one is wise in the ways of the world (think: Machiavelli) can be predicted with a high degree of confidence from the designs and processes it institutes.
Thus, it is perfectly possible to fondly dream of a brotherhood of man and yet, based on some combination of practical political analysis and real-world outcomes, loath the United Nations. Once again, the ends – a united world – is not what is being criticized or defended. Only the means – the UN – is subject to criticism, for example on its track record of delivering a more unified world. Perhaps world unity will never be established by means of a gigantic bureaucracy? Bears thinking about.
Same issue arises with the EU, and, indeed, with all leagues and organizations that have some noble goal as part of their names. Pournelle’s Iron Law necessarily results in any large bureaucracy becoming its own goal over time – regardless of how much its name suggests some finer goals or tugs on our heartstrings.