Self-Actualization: Becoming a parent is a life goal for many because it becomes part of their identity. If a character believes they're incomplete because they have not yet felt that parent-child bond, it would drive them to find a way to do so.

Esteem and Recognition: Some people find themselves in situations where having a child is an expected duty, and there is a lot of pressure for them to follow through. A character who believes their self-worth is tied to their ability to procreate would be desperate to have a child so they could prove their value to their harshest critics (and themselves).  

Love and Belonging: This need may be a driving factor for characters who love deeply and want to shower that affection on a baby, or for those who feel that their existing loving relationships will be at risk if they remain childless (e.g., a partner threatening to leave if the character doesn't agree to pursue this goal).

Safety and Security: Sometimes having a child is more about ensuring future security than it is about becoming a parent. A character (most often a female) may try to get pregnant in order to secure finacial stability from their partner, especially if this is something they are deeply worried about (because they are unable to provide for themselves, they have been mistreated and so safety is an ever-present concern, or they have suffered past hardships and refuse to do so again). 

Physiological Needs: In extreme situations, a character may fear for the future of their race and so feel driven to procreate. The need to propagate the species is a hard-wired survival instinct and is difficult to ignore. A more common scenario is when a character ages or has a brush with death, and they realize that they won't live forever. In this case, they may be driven to have a child so a piece of themselves will live on.