In The Case Against Mortality, Leon Kass argues that mortality is fundamentally a blessing.

The second argument against mortality is that only mortal beings can have serious lives. By serious life, I mean a leading a life that fulfils its telos. From this statement, one might raise the nihilistic counterargument that life may be purposeless. Hence, in this case, leading a serious life would mean embracing such purposelessness. I will not attempt to determine whether or not life has telos and if so, what it is. Thus, I will consider both situations: that life is purposeful and that it is purposeless. Firstly, assuming arguendo that life has a certain telos, is death a part of such telos? In Christianity, for instance, death is part of the greater purpose of God, "and we know that in all good things God works for the good of those who love Him, who have been called according to His purpose." (Romans 8:28) It is also believed that after the earthly death, there is an everlasting afterlife in the kingdom of heaven, so "after that [death], we who are still alive will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever." (Thessalonians 4:17-18) Therefore, prolonging earthly life indefinitely would  actualy prevent one from fulfilling the higher purpose of an everlasting life in Him.

 Nonetheless, even if one believes that the meaning of life is secular, immortality might still compromise it. Take it that someone finds meaning of life in acting virtuously. In essence, one is spending one's time on earth, sacrificing one's life, with something one deems important, such as helping those sleeping rough. If one can possibly live indefinitely, one would not be giving up his time to help the homeless, but rather helping them without any sacrifice. Although the outcome may be the same, it is easier- and possibly less valuable- to help someone only to the extent it does not affect the helper. Therefore, one would act virtuously insofar it is convenient, which might jeopardise the sense of fulfilment one derives from acting virtuously. It might be the case that one would still be spending one's life helping the homeless for humans would still die in accidents, and would, hence,  derive the same satisfaction. However, as Martha Nussbaum argues, "the further mortality is removed, the further they [the virtues] are."

Now, assuming arguendo that life is uterly purposeless, immortality still poses a threat to seriousness. Albert Camus argues that life is absurd, i.e. although humans try to derive meaning from life, it is meaningless and chaotic. Still, he believes that one ought to embrace the meaninglessness because of life and that life is still agreeable and worth living because of its little pleasures, e.g. kissing, sun, and pleasant aromas. But for how long are these small pleasures capable of preventing one from killing oneself? And can the extreme prolongation of such small pleasure actually ruin them? Gilbert Meilaender compares life to a banquet, "having a stopping point beyond which the banquet cannot be prolonged without destroying its pleasures." Ovid also comprehended the role of time, and wrote that "time [is] the devourer of all things,"  and I suppose that would include the small pleasures. As much as one likes to believe that, as Virgil puts it, amor vincit omni," if there is something that even love cannot conquer, this thing is time.

Immortality is also a menace to beauty. The poet Wallace Stevens wrote that "death is the mother of beauty."  Although many different meanings can be impressed upon this quote, I believe that it is better understood alongside with what Rainer Maria Rilke wrote: "beauty is only the beginning of terror, which we are just able to endure, because it so serenely disdains to annihilate us." This correlation between beauty and terror was depicted by Edmund Burke, who called the beauty that is rooted in terror sublime. He wrote that: "Whatever is fitted in any sort to excite the ideas of pain, and danger, that is to say, whatever is in any sort terrible, or is conversant about terrible objects, or operates in a manner analogous to terror is a source of the sublime; that is, it is productive of the strongest emotion which the mind is capable of feeling." Therefore, following this line of reasoning, death must be the greatest source of terror in life, making both life and death, as terrible as they might be, sublime. In the same way a storm terrorise us, it does not fail to beguile us, just like John Mill's description of Satan: "Less than archange ruin'd, and th'excess/ Of glory obscured: as when the sun new ris'n."  However although one might agree that terror and beauty are closely related, one might suppose that there is neither beauty nor sublime in death. One might claim that death is horrid and it must be vanquished. To that, I will respond with what Oscar Wilde wrote that "Yes, death. Death must be so beautiful. To lie in the soft brown earth, with the grasses waving above one's head, and listen to silence. To have no yesterday and no to-morrow. To forget time, to forget life. To be at peace." 

Insofar, I have argued that there are thre main problems with immortality. The first is the problem I called tædium vitæ, which I defined as being weary of life. It would happen because being conscious and awere of oneself is very tiresome, and one would eventually long for the oblivion of death. The second problem is a threat to seriosness, which is leading a purposeful life or embracing its purposelessness. In the first case, acting virtuously depends on having a finite life because otherwise, one has no reason to not become a hedonistic. On the second, it is impossible to embrace the purposelessness of life for an indefinite period of time because time makes the little pleasures that make life agreeable abhorrent. The third problem is that beauty depends on terror, and the utmost source of terror is death. Hence, the death of death would be also the death of beauty. Considering all these arguments against immortality, one might wonder why would anyone ever desire immortality then. Although Kass argues that a desire for immortality is actually a desire for completeness, I believe that no one desires immortality.

The german neurologist Sigmud Freud argues that the "the goal of all life is death." He claims that before birth the being was in a state of non-existance, and such state was interrupted by birth, which brought the being into a state of existance. Hence, beings aim at returnunig to such state of non-existance by death. Such death drive, which would later become known as thanatos, is conterpointed by a drive towards life, which is known as eros. Together, thanatos and eros put humans in a state of stasis. Therefore I believe that a desire for immortality is merely a manifestation of the eros. However, were immortality truly achieved, such stasis would be interrupted. Hence, thanatos would manifest itself by a desire towards death, bringing humans into stasis again.

Therefore, albeit Leon Kass was most likely right to claim that mortality is a blessing rather than a curse, there are more solid arguments on which one can defend that. I have attempted to argument against immortality on the most substantial basis I could think of: that an eternal life would be filled with tædium vitæ, lack  seriousness and beauty, and that immortality is not desired, it is rather a repetion ritual in which one tries to derive some comfort from the loss of pleasure. However, were immortality truly possible, the pleasure one derives from it would soon become displeasure and one would long for death. Still, this argument is rather conjectural for there are no immortal human beings.