Final answer:
Don Vito Corleone is shot because he denies entering the narcotics trade with Sollozzo, leading to an assassination attempt to remove his influence and coerce the family into compliance.
Step-by-step explanation:
In The Godfather, Don Vito Corleone is shot due to his refusal to enter the narcotics business with Sollozzo. Sollozzo, backed by the Tattaglia family, believes that Corleone's influence can boost the drug trade, but Corleone believes it's a dirty business that will ruin his political connections.
After his refusal, Sollozzo makes an attempt on his life to take him out of the equation and to intimidate the Corleone family into cooperation.