Why does Gan choose to accept his “responsibility” to T’Gatoi?

Gan has very little choice in the matter. He lives on a planet where Terrans such as himself are impregnated by giant insect creatures called the Tlic. This is a long-standing tradition in which Gan is expected to play his full part. To make matters even more complicated, Gan's family has a very close relationship with one of the Tlic called T'Gatoi. The Tlic are ultimately dependent for their survival on the Terrans. If the Terrans don't incubate the Tlic's eggs then they will eventually die out.
Likewise, being impregnated is an important rite of passage for Gan. This will be his entrance into adulthood. Although he's understandably apprehensive at the impregnation procedure and all that it entails, like any self-respecting boy of his age he wants to be accepted as an adult. For all his reservations about the birthing ritual, Gan knows through his upbringing that the Terrans are guests on this planet and depend on the Tlic for their security and well-being.