I have a piece missing from my self. I am sure a lot of people feel the same way. I know others don't: their self is complete. They could feel happy, or unhappy, in particular situations, but their self is basically a complete entity. In the same way, I can feel happy, or have good day, but that doesn't mean I am a complete person.
You can try to fill the missing piece with drugs, alcohol, work, religion, or a relationship; any one of a number of things. That will not really fill the gap, though. The gap is in you (or me, in this case), so nobody or nothing else can fill it up. People have names for the cause of this gap: the patriarchy, capitalism... Those things may be bad, but they are not the cause of the hole.
I have no idea of why I feel this way, but I almost always have felt so. I cannot even complain about it, because I'm assuming the a certain percentage of people walking around on the street are in exactly the same position as I am. In fact, it gives me some satisfaction to let you all know that this is the way I feel. I will no longer pretend to be a complete person.
You may feel the same way but give a different label to the experience. My particular name for it is this, but you might must feel that something is wrong with you.