In the history of science, this was widely believed as it was accurate to the present level of understanding - however, this began to fall apart after the dawn of quantum mechanics.
Before the Heisenberg uncertainty principle, it was scientifically correct to say that if the position and momentum of every particle in the universe was known, the past, present and future could be predicted with absolute (analytical) accuracy. This was known as determinism (the theory you champion here) This was proven to be false as there exists an intrinsic uncertainty with respect to position and momentum on a very small but non-zero order.
In practical terms, this is demonstrated by the many body problem. The energy levels of any atomic system with more than one electron cannot be analytically determined - it can only be approximated. The energy levels of the hydrogen atom, and the He+ ion, Li++ ion, etc. can be precisely determined but nothing with 2 or more electrons, this is because electrons interact with each other (repel) and the intrinsic uncertainty of the position and momentum of one has an impact on the energy level of the other.
This means the brain is not deterministic. It's random at best. But we also know that the hypothetical free will of a person is not random, which means scientifically that there must be an unaccounted-for transcendental property of the brain, commonly known as a soul.
The non-deterministic values of quantum mechanics are not proven. Thats a theory. Many scientists suspect deterministic values we cant measure. Also, Soul is absolutely not a scientific term at all.