How does the Miller-Urey experiment fall short of demonstrating that life can arise from inorganic molecules?

Answer: The Miller-Urey experiment falls short of demonstrating that life can arise from inorganic molecules in that: It doesn't show a leap between a collection of amino acids and a single-celled organism

Miller and Uray experimented with methane, ammonia, and carbon dioxide in a laboratory condition. Then he keeps them in an experiment environment and applied high electric current to this mixture of 3 gases. After the passing of electric charges in this gas mixture, the molecules are split. After some time this results in another element such as oxygen, amino acids, and water.

Water, amino acids, and water are the essential components of life. Every living animal cell has amino acids and they need water, oxygen for their survival.

His experiment shows life arose from non - living components. Because in this experiment he created the environment of the beginning of the earth's atmosphere. At that time no oxygen and water were there. Heavy lighting causes the splitting of the methane, ammonia gases along with co2. This creates water and oxygen and also cause heavy rainfall. This rainfall continues for several years to cool down the hot earth. Then the holes of the earth filled the forming ocean and new life arose in it.

That's why Miller and Urey's experiment shows life arose from nonliving things.