John Searle accepts the human brain is a computer of sorts, but rejects that it is like current digital computers. He believes there's something inherently different between the biological causality of the brain with the universe and that of the digital computer with the universe, and so while both brains and computers have similarities, only brains can manifest "aboutness" (intentionality) about the state of affairs, he believes that physical causality is larger and different than the digital models, read Turing machines, we build of it. That difference is best understood as consciousness. He believes computers only dissimulate consciousness, which is the default position of many philosophers and can be traced back to Descartes and his views on the exceptional nature of the human mind. One particular view is that only humans have a soul, and not even animals truly reason. (See "Quotations from Descartes on Animals as Automata" (PhilSE).) Philosophical debate of Cartesian dualism is fundamental to an understanding of contemporary philosophy of mind.
Alan Turing once proposed his Turing Test and a timeline to show computers would quickly mimic the capacities of the brain. He would be profoundly disappointed that Hubert Dreyfus convincingly argued in his What Computers Can't Do: The Limits of Artificial Intelligence published in '72 that Turing was wrong. Searle is a relatively orthodox philosophical thinker who is skeptical that digital computers can ever fully represent the human brain and manifest consciousness, taken to be a necessary condition of intentionality. He is famous for his philosophical problem, the Chinese Room to advance his skepticism.
In his book The Mystery of Consciousness he says on 294:
[T]he essence of consciousness is that it consists in inner qualitative, subjective mental processes. You don't guarantee the duplication of those processes by duplicating the observable external behavioral effects of those processes.
This notion of computers possessing intentionality has even more challenge to it than overcoming radical solipsism where philosophers like David Chalmers have come up with philosophical ideas like philosophical zombies and the hard problem of consciousness to continue the tradition of the Ancient Greeks of making the fallibilism of knowledge evident through skeptical argumentation.
On the other end of the spectrum are more progressive thinkers like Alan Turing who believed in broad notions of artificial intelligence that might qualify him as a believer in artificial general intelligence which is a body of thinking that computers can be every bit as sentient and possess intentionality as people, broadly in the spirit of functionalism in the philosophy of mind. (Warning, my biases are with the AGI crowd: see See my response to Computers, Artificial Intelligence, and Epistemology). It's a matter of fact that a small but active community of cognitive scientists and philosophers are trying to advance a philosophical thesis to prove Searle wrong about how consciousness can be simulated.
As such, John Searle is largely in line with the orthodoxy in the broader analytic philosophical community expressing skepticism of the possibility that digital computers have or will ever have intentionality. Some interesting proposals have been advanced by thinkers who agree with Searle to come up with the missing part, Roger Penrose and his The Emperor's New Mind being an excellent example. In his thesis, there are quantum properties to neurons that are not represented by deterministic state machines that merely manifest computability.
Part of whether one believes Searle is wrong or not has to do with metaphysical presuppositions and first principles that are involved in the philosophy one does. Since computers are essentially composed of microprocessors ALU-CU-MMUs that compute formal systems, one's philosophy of mathematics can be used as a bellwether of sorts. For instance:
The association mechanism involves causal properties (of the brain and body). "Semantics" is a very ambiguous word, formal semantics is of a kind with formal syntax, at best, it "relates" one abstraction to another, not to anything real. - Conifold
It is arguable that formal semantics doesn't somehow relate to "real things", as every model-theoretic construction using the formalism of truth-conditional semantics is can be thought of as an abstract mathematical object used in the spirit of applied mathematics to model something real in the physical universe. Philosophically, mathematical constructivists see all formal systems including formal semantical models as rooted in the psychological experiences of the mind.
Whether or not it is possible to simulate a human brain is controversial in artificial intelligence, with one crowd believing that AI will never consist of anything more than symbolic systems and machine learning that will twiddle bits, and the AGI crowd believing that as soon as cognitive science provides insights that will allow machines to approach, attain, or even pass human intelligence, it will come to pass. The last position was made most famous by a futurist and computer scientist Ray Kurzweil who in transhumanism and the singularity as argued for in his The Singularity Is Near.