I have a dear friend who is struggling lately with that age-old question: "Who am I?" I am horrible with a verbal explanation of such mysteries; I always end up feeling like I don't sound like myself, and I fear the potential rejection of this facet of myself, so foundational to the whole, and yet, for much of my life, so private and intimate a piece of the whole. So, I will try to answer here, in the format where I speak the best.
Your problem, my dear, is your focus. It always has been. Your center is yourself, and you will never find the meaning of your life within yourself, no matter how logical that might seem. You will only find true, unshakable meaning in your life by changing your focus. When you realize that the question is not so much, "Who am I?" but rather, "Who was I created to be?" then you will be on the right track. That question, I can answer, and know without a doubt that the answer I give you is true and correct.
The answer is love.
You were created from love, you were created by love, and you were created for love.
You were created by God, who is Himself the very essence of love, in its purest, truest sense. The very reason for your creation was love. Your very life is a product of love. I don't speak of the love between your parents. Heaven knows, some of us can claim to be the product of our parents' love, while others cannot. Does that make their life of any less worth? No, for the love I speak of is the love, not of the parents, but of the Creator. The parents may "create" your mortal body by their actions (though even this is not without God's consent), but God Himself forms your immortal soul. Now, God, in Himself, is complete. He lacks nothing; He needs nothing. You were not created by Him because He needed your adoration, your worship, your service, or even needed you simply for His own amusement. You were created because of His great love for you.
And you were created for love. You were created to know love, and to give love--first and foremost in your relationship with the One who created you. You were made, and you are meant, to know His love, and to love Him in return. He has loved you since before the moment of your creation, much like parents may love a child before he is ever born, or indeed before he is conceived, if they have waited and struggled to have children. But you will never be complete until you accept that love, experience it, know it. Once you accept that love, a wonderful thing happens. You can return it. And more, you can give it to others.
When asked by the religious leaders of his day to name the greatest commandment, Jesus answered them, "Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the first and great commandment. And the second is like unto it, thou shalt love thy neighbor as thyself. On these two commandments hang all the law and the prophets." (Matt. 22:37-40) You were created for love.
You were created to love God, and to know His love. You were created to love the people you encounter in your life. Some of them will love you back; you were created for that as well. Others will not; that's okay. You were still created to show them love. Jesus also said, "Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy. But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you." (Matt. 5:43-44)
You were created to receive God's love in such a way that it spills over onto everyone you meet. Notice that we must first receive if we are to give. You cannot give to others what you have not first accepted from His hand for yourself.
The center of it all is love. And God is love. So, it naturally follows that the center of it all--is God. That is what you were created for; that is who you are. The rest is just details.