Genuine re-incarnation is the descent of divinity into a human being. In order for the Innermost, the Spirit, to reincarnate, his Soul needs to build Astral, Mental and Causal Solar Bodies. The incarnation of Christ into a human being is what is called an Avatar. In Hinduism, Vishnu is the Christ, the Solar Logos. This is why in India they say that reincarnation is performed by Vishnu. Krishna spoke about this, by saying: "Only the Devas reincarnate."
"Thus, reincarnation is a feat accomplished only by the great illuminated souls, in which they consciously choose to be born in a particular time and place; in other words, they chose to incarnate the Being in a new physical body. Only beings with conscious development can do this. The word reincarnation is most demanding, it must not be used carelessly: No one would be able to reincarnate without first having eliminated the ego, without truly possessing sacred individuality. Incarnation is a very venerable word, signifying in fact the reembodiment of the Divine in a man." - Samael Aun Weor, The Mystery of the Golden Blossom
The rest of us do not reincarnate: we return.
"We should not mistake the Truth with opinions. Many think that the Truth is this or that, or that the Truth is within this or that book, or within this or that belief or idea, etc. Whosoever wants to experience the Truth should not mistake beliefs, ideas, opinions and theories with that which is the Truth. We must experience the Truth in a direct, practical and real manner; this is only possible in the stillness and silence of the mind, and this is achieved by means of meditation."