why egyptians threw away their their brains

  Ancient Egyptian mummies had no brain.  It was discarded with the blood. All other organs were preserved in canopic jars beside the mummy. This style of preservation for eternity was carried out from about 3500 BC and became popular even for middle-class Egyptians till about 500 AD. But no-one ever thought to keep the brain. Perhaps, like early Greeks, they regarded it as a heat sink.
          Mummies are no longer unwrapped. They are CT-scanned. This reveals not only bones and surviving tissue, but often dozens of objects called ‘amulets’. These are now scanned at high resolution and 3D-printed for examination. A flat anatomically shaped golden tongue is common - presumably to enable speech in the afterlife. An amulet shaped like two fingers is often placed by the incision where organs were removed. Others aren't anatomically shaped, and are found spread throughout the body, sometimes made of clay. They can be shaped like scarabs (representing the resurrection god Khper), or tiny flasks, cylinders, pebbles, or like the eye of Horos.
         The heart is represented by the largest amulet, often inscribed with parts of the Book of the Dead.  The heart was considered the centre of thought and intentions in the ancient world. The Egyptian god Ma'at weighed the heart to see if it was heavy with sin.
            So the brain was inconsequential. Ancient Egyptians didn't even have a word for it. The Bible doesn’t mention the brain either. It talks about the mind and thoughts, and even Jesus says they come from within our hearts (Matthew 15:19). This isn’t inaccuracy - he accurately conveyed his meaning in terms his hearers understood. Jesus taught salvation, not science. 

Article:
www.sciencealert.com/ancient-mummies-with-golden-tongues-revealed-in-stunning-discovery 
Paper on the modern process and an example:
www.frontiersin.org/journals/medicine/articles/10.3389/fmed.2022.1028377/full