Krishna names the destination: immortality. The person who is not thrown off balance by pleasure and pain — who remains steady when life swings between the two — that person, O best among men, is fit for what is deathless.
Remaining equal does not mean feeling nothing. It means not being controlled by what you feel. A seasoned sailor feels the storm as much as anyone on the ship. The difference is that the sailor does not abandon the wheel. Steadiness is not numbness — it is composure under pressure.
The word 'amritatva' — immortality — does not mean the body living forever. It points to the recognition of the soul's eternal nature. When you stop being tossed by every wave of pleasure and pain, you begin to glimpse what in you has never changed. That recognition is itself the doorway.