I believe that I exist because I have a purpose to fulfill. My first purpose was to be the wife of a terrific man who pushed me to be all that I could be, and the mother my family needed with all the medical issues that entailed and all the doctors I needed to push to find answers. I needed to love and protect my family from those who saw the issues as imaginary or as an over-protective mother. Thankfully, I made it through, and my family is now as healthy as hoped. My grandchild is as much fun as I expected!
My second purpose was to be the teacher I was, who always brought my A game to every year and all of my students. I believe that even with some mistakes, I made a difference and taught writing with a flair which eighth grade students could grasp and utilize.
My third purpose is this life is to listen. As a jail crisis volunteer, I provide a listening ear without judging the person. Judging is for the courts and God, not me. Having long experience with mental health issues both in my family and my teaching career, listening well is an art form in the jail. I know that this is something I must do, for so few do it at all and the need is so great. Perhaps there is another purpose for me, but that will reveal itself in time.
I exist, from a biological standpoint, because my parents procreated.
More importantly, I exist because a Creator God desired to develop a special type of relationship with the results of Creation. The first book of the Bible, Genesis, records two different stories to explain how humanity came into existence. The first, more general version, suggests that God created "man in his own image...male and female He created them" (Gen. 1:27) because God wanted someone similar to God to care for all that had been created. The second version tells that God created man "in the Garden of Eden to work it and take care of it" (Gen. 2:15) and later created woman to be a companion for man.
People, including me, exist because God desired to have a loving relationship with what had been created. As I try to give glory to my God and care for the creation around me, I fulfill the reason for my presence.
To be perfectly honest, I don't know that I can answer this question from a religious standpoint. If I take my birth religion as Truth, then I would say that humanity exists because of God's desire to create, and from the need of a Creation (Man) to have free will so as not to be puppets on a string but to honestly and genuinely come to their decisions. However, I have been going through various forms of existential crisis in the last few years, and I can't give the above as my personal answer. Instead, I will say that a person's personal religious beliefs are the basis of their entire personal philosophy; if there is no religion, philosophy must by definition come from a secular viewpoint. We can justify our existence through religion, but considering the vast needs of the species as a whole to continue expansion into the larger universe, I would justify Humanity's existence simply by pointing out that, as of yet, there are no other intelligent, sapient species in the world.
I do not think that there is any logical way to say why we exist and what the purpose of that existence is. Of course, as the previous post says, it is because our parents procreated, but I don't think that's a serious answer because that doesn't explain why the whole universe exists in the first place. The Big Bang Theory can explain how the universe came to be but not why.
If we believe in God, our purpose for existence is to fulfill his plan for how the world and the universe should be. If we do not believe in God, then perhaps the purpose of our existence is simply for us to enjoy our lives and live the best possible lives that we can while we exist.
Logically, we exist because our parents got together and procreated, and they likely did so because procreation is an evolutionary imperative. Our purpose, logically, is to live our lives as we see fit.
Normally Christians believe in one creator God, threefold in being (Father, Son, and Spirit). The Son is the Logos or Wisdom of God, the archetype of all creation, who was incarnate in Jesus… (enotes, Christianity)
Religiously, we exist because God created man in his image (or whatever your religion says). Our purpose is to serve God and behave as we have been mandated by our particular religion.
Each person has to answer these questions for his or her self. You have to find your purpose in life. Some people go an entire lifetime without finding it, and some people never look. That is a purpose too, I suppose.