Why is a very large initial metacentric height not automatically best for a passenger ship?

Answer: A very large metacentric height makes the ship stiff, so it snaps upright and rolls uncomfortably fast.

A very large metacentric height makes the ship stiff, so it snaps upright and rolls uncomfortably fast. ✓ — Right. A very large metacentric height gives stronger initial righting arms, but too much makes the ship stiff: it snaps back quickly and can create uncomfortable accelerations. Passenger ships want enough stability, not maximum stiffness. The design target is a comfortable margin, not the shortest possible rolling period.

A very large metacentric height gives a bigger safety margin, so passengers feel safer and more comfortable. — Close, because safety matters, but comfort does not simply increase with metacentric height. A larger value strengthens initial righting, yet the same stiffness can make accelerations harsher. Passenger ships need enough margin to satisfy stability rules without turning every small roll into a sharp snap-back.

A very large metacentric height lengthens the roll period, so the ship sways slowly and gently. — No, slower and gentler rolling is usually the behavior of a more tender ship, not one with a very large metacentric height. A large metacentric height shortens the natural roll period, so the ship returns quickly and can feel abrupt. The tradeoff is that stronger self-righting can come with a less pleasant ride.