The immortality would mean you can not die, but doesn't mean that you can not get hurt, so even if it exists, trust me it's not that you would like in the long run, just imagine falling from the airplane becoming paralyzed or/and without limbs and just suffering for years in constant agony, as you wouldn't be able to die.
Or imagine being stuck somewhere underground for decades without light or any sort of food that would keep you in shape.
There is also quite popular theory about quantum immortality, you can find more on that on google.