The built-in incapacity of consciousness to comprehend its own limits -- that is, to stand outside of itself and observe its own "shape" against a background of not-self, to perceive itself as one perceives any empirical object -- leads to the metaphysical, solipsistic
feeling that one's subjectivity must be immortal, immutable, limitless, etc.
The contradiction between this solipsistic feeling and the rational admission or deduction of one's finitude (e.g., I am a person and people invariably die and so I'm going to die too) produces a series of questions, all of which express the same desire -- namely, the desire to resolve that very contradiction. Such questions include, "Why am I here?", "Who am I really?", "What's my purpose in life?", "Why do I exist?", "What's the meaning of life?", "Why is there something rather than nothing?", "Why am I a part of that something?", and so on. The presupposition that it is possible to answer such questions, however, makes the (logical-grammatical) error of attempting to "make sense" of that which serves as very ground or condition of the possibility of sense in the first place. Existence and awareness are given, simply, and nothing more can be said or thought about them as such, no matter how strong the metaphysical feeling is. The original, primordial anxiety that Heidegger speaks of is precisely the "pain" -- a pain or dissonance which is simultaneously cognitive and emotional -- of this contradiction. Religion has been termed an irreducible "ontological madness". I don't recall the source of this definition (though I believe it was referenced in Sloterdijk's Critique of Cynical Reason). I would, however, posit that religion is, rather, the result of an attempt to compensate for the ontological madness which is precisely this pain, this contradiction, this anguish, this rift, built-in to the structure of consciousness itself.
I would posit that there are at least three possibilities for an authentic confrontation with this contradiction. The first, I'd suggest, would amount to a sort of madness -- it would consist of sharpening this contradiction, of opening the wound and crawling inside of it, of insisting that a solution can be found, and of devoting all of one's effort to finding it. The way of the metaphysician or Heideggerian, perhaps. The second would be Wittgensteinian -- to recognize the grammatical-logical error in the question itself and to train oneself to "see the world aright". And the third, of course, is to posit that our finite consciousness is sustained by a kind of infinite, existential consciousness which, because it is infinite and self-caused/self-sustained, has a perfect comprehension of itself and doesn't suffer from the pain of an internal, structural contradiction. It should be noted that this infinite consciousness could be either transcendent-dualist (religious) or immanent-monist (Spinozist).
The first option, I think, is a kind of a default -- what happens when one is faced with the anxiety of the contradiction but can't decide whether to take a Wittgensteinian, religious, or quasi-Spinozist approach to it. And I suppose that we could posit a fourth way -- that of ignoring the contradiction, of losing oneself in the distractedness of what Heidegger might call "everyday Dasein". But I don't think this way is sustainable. Repressed "existential anxiety" always returns in one way or another.