I person can say "I define myself as citizenshipless" (more often called being stateless), but saying so does not make it legally effective, Most people on earth get citizenship somewhere at birth, either by place (ius soli) or by decent (ius sanguineus) Some get more than one citizenship, or can squire an additional one later.
Each country defines citizenship via its laws, regulations, and administrative actions. If a person P is a citizen according to the laws of country A, that person remains a citizen unless something happens that changes that status. That may be some thign that P does, or it may be something that country A does, oe both. But as long as A says that P is a citizen, A's laws will treat P as a citizen, including any obligations.
Some countries, such as the US, allow a citizen to make a formal declaration, in front of an official, that the citizen renounces citizenship, and this ends P's citizenship. Some countries will terminate P's citizenship if P applies for citizenship in country B, or join's B's military, or commits one of a list of crimes, or fights in a war against A. Some countries have at times passed laws declaring that specific people, or members of specific groups, are no longer citizens. And some countries may not have any way for P's citizenship to end.
In the end it is the laws and official declarations of the country that count. Citizenship is a legal status, like marriage or holding a particular license. Like those, it is the laws and any implementing regulation of the country A that define it in that country.
Note that A may consider P a citizen of A, but country B may not. Each country's laws will apply in that country.
Being stateless that is, not being a citizen of any country, usually has significant disadvantages, but some people have intentionally become stateless.
I assume that citizenship is any time period in which all officers (or enough officers) of a given state would agree to issue citizenship documents (for example, a passport) for that human.
Not correct. There are several reasons why a county might refuse to issue a passport or other document that certifies citizenship to a person who is nonetheless considered to be a citizen. Most countries will not issue a passport to a minor. Some countries will not issue a passport to a person who has been convicted of certain crimes. Many countries will not issue a passport to anyone awaiting trial on a serious crime. The US has, on a number of occasions, refused to issue passports to people whose political opinions it disapproved of, when it did not want them making speeches outside the US. Other countries might act similarly. As to other documents that indicate citizenship, some countries do not really have any, others do. But many have requirements beyond bare citizenship for issuance of such documents..