Example: Countries usually frame their citizenship laws with little or no regard for the citizenship laws of other countries. In my son's case, for instance, the US does not care that Canada thinks he is a Canadian citizen, and Canada does not care that the US thinks he is a US citizen.
In some (but, please note, not all) cases, a country may seek to restrict dual citizenship by requiring one of its citizens born with some other citizenship to renounce (give up) the other citizenship upon reaching adulthood. Similarly, newly naturalized citizens in some (but not all) countries are required to renounce their previous citizenship(s); the US has such a requirement, for example, but Canada does not. And in some (but, again, not all) cases, a country will automatically revoke the citizenship of one of its citizens who acquires another country's citizenship by naturalization, even if no explicit renunciation was involved.