One has to think logical, before he can understand the answer to this question.
What is soul ( Atman ) ?
नान्योऽतोऽस्ति द्रष्टा, नान्योऽतोऽस्ति श्रोता, नान्योऽतोऽस्ति मन्ता, नान्योऽतोऽस्ति विज्ञात, एष त आत्मान्तर्याम्यमृतः, अतोऽन्यदार्तम्; – Brihadaranyaka Upanishad verse 3.7.23
“He cannot be seen, but he is the seer; He cannot be heard, but he is the Hearer; He cannot be thought, but he is the Thinker; He cannot be known, but he is the Knower. He is the Internal Ruler, your own immortal Atman. Everything else is destroyed except the Atman”
- Rebirth cannot belong to the soul,because as per Bhagavata Gita 2.20 the Soul (Atman) is never born nor it dies.
न जायते म्रियते वा कदाचि न्यायं भूत्वा भविता वा न भूय: | अजो नित्य: शाश्वतोऽयं पुराणो न हन्यते हन्यमाने शरीरे
– Bhagavata Gita 2.20
“The soul is neither born, nor does it ever die; nor having once existed, does it ever cease to be. The soul is without birth, eternal, immortal, and ageless. It is not destroyed when the body is destroyed”
- Rebirth cannot belong to the Physical Body, because it is non-living thing without the Atman, it has no consciousness and has no existence. ( consider physical body as shirt and Atman as person who wears it, does shirt has rebirth ? )
So neither the Soul (Atman) is reborn nor the physical body.
Than why we believe on rebirth ?
Because it is belief caused by Maya. We consider this body as Real, and its birth and death as Real. Upanishads says that you are not the body, but the Atman which is never born and die. Understand this identity with body is a wrong assumption.