There are many countries that do not have any process in place for renunciation of citizenship, or that require some special approval that is seldom or never granted (e.g., Iran). 

 Even countries that do allow people to renounce citizenship (e.g., Canada, USA) make it difficult and often expensive to do so.

Telling people that they simply renounce their original citizenship is to aks them to do something that is often either extremely difficult or impossible.