Why do people use all 3 components in their gender pronouns?

Solution 1:

People who have gender identities that conform to their biological sex (oft referred to as "cisgendered") can show solidarity with the trans community by offering our own pronouns whenever appropriate, thereby helping to normalize the practice. If all trans people used "he," "she," or "they," simply giving a nomative pronoun would allow the listener to extrapolate all other pronouns. However, some trans people prefer to use Neopronouns, which don't always declinate in a intuitive way, such as e/em/es or thon/thon/thons. Neopronoun users give their nomative, accusitive and predicative possessive pronouns out of necessity, so those of us using standard pronouns follow suit.

Solution 2:

There are now a number of additional pronouns, mostly used by people who identify as non-binary (neither 100% male, nor 100% female, or a third gender). Most people are not familiar with them, so don't know how to use them when only one is presented. If one pronoun is "xe" or "chis", what are the others? Can you work out the rules without being told?

The generally accepted pronouns are not regular, in fact they're highly irregular so they have to be memorised. Most people have not had enough exposure to these additional pronouns to have memorised them and be familiar with them.

This is why two, three, or even the full set of five pronouns will be mentioned.

Solution 3:

Not all people want others to use the standard pronouns, whether masculine feminine or plural. Other possible pronouns exist such as ze, hir, zirs etc. Many people are unfamiliar with the usage of those and what the object and possessive forms are, so it makes sense to specify all of the ones you want to be called by in each circumstance.