Being immortal would be great. I know what it's like to be alone, and I'd rather be alone forever than die. Just as long as it's not like Twilight.
We are not immortal in the same way as God, who is immortal without beginning, and remains so of Himself,but we are immortal as far as having no end, and remaining forever as He designed. We die (formerly and more accurately 'pass away'), but we never really die. We go to a better place, another accurate phrase fallen out of favor by man's rebellion against his Creator.
Earth will eventually cease to exist. So if your are immortal eventually you'll just be floating around in space forever and depending on whether or not you can feel pain you would be constantly gasping for air. It wouldn't even have to be the world ending to be in hell if you were to fall into a hole or something you couldn't get out of you'd just be stuck for years. Death is a sweet release.
Living forever releases the weight on your shoulders to make any sort of accomplishments with your life. Why fall in love, when you will outlive the other? Why exhaust yourself when you never get the satisfaction of resting? There is no meaning to life when you don't have to worry about what comes after.
Have you seen Tuck Everlasting(2002)? Or the Age of Adaline? The characters who had immortality hated it; they outlive everyone around them. Everybody else grows old and dies while they live on, that has to be unbearable. In Tuck Everlasting, Angus told Winnie; "Don't be afraid of death, be afraid of the unlived life. You don't have to live forever, you just have to live".