Why can some comets enter the solar system and then never return?

In the context of celestial mechanics, comets that enter the solar system and never return are typically those that have been gravitationally scattered onto hyperbolic orbits.12

When comets pass through the planetary region, they are subject to the gravitational influence of the giant planets, particularly Jupiter. These gravitational perturbations can alter a comet's orbital energy, either capturing it into a shorter-period orbit or increasing its velocity to the point where its orbit becomes hyperbolic. Once a comet enters a hyperbolic trajectory, it is no longer gravitationally bound to the Sun and is ejected into interstellar space.21

Additionally, many comets formed in the outer regions of the solar nebula were ejected by the gravity of the growing giant planets during the solar system's formation; the vast majority of these were sent on hyperbolic paths to interstellar space, while only a small fraction were captured into the Oort cloud.1