People have different reasons for why they want to obtain an EU second citizenship. The Treaty of Maastricht states that Every person holding the nationality of a Member State of the European Union is, as a result, a citizen of the Union. Citizenship of the Union supplements national citizenship without replacing it.
This clause from the Treaty of Maastricht means that an individual who becomes a citizen of any EU country is granted EU citizenship automatically. EU citizenship is not a separate "national" citizenship, but is related to the individual's rights in any of the EU countries.
There is a difference between becoming a citizen and a resident of any EU country. Citizenship is normally obtained through birth, marriage, long-term residency and family relations. Only citizens can obtain a passport. A resident with the legal right to live and work in an EU country holds a foreign citizenship and passport. However, if you want to obtain EU citizenship as the second citizenship, you should learn citizenship rules of the country you are interested in. But dealing with foreign governments in a different language is not always easy. However, it is easy to make an appointment with an EU immigration professional and get a consultation in relation with EU second citizenship and answers to all questions quickly.