How could something striking the earth million years ago have killed all the dinosaurs?

When the asteroid hit, it launched a huge amount of dirt and dust into the air. This blocked out the sun over a large area, and that caused the Earth to become colder. The colder weather caused many plants to die. Without the plants to eat, many of the animals that ate the plants began to die, and then the animals that ate those animals, and so on down the line. Essentially the food chain collapsed from the bottom up.