Why do insectivorous birds migrate?
Reason for Migrating Birds:

Migrating for a Meal

Food scarcity: If birds will stay and eat all the bees they find, there will be no bees to feed on for the next generation. So, they fly away to take advantage of these places where there is abundance of food. And when the insects or replenish they come back.

Migrating for Family

Flocks of bird can be easy prey as they are small and are in a huge number. Also for the young ones who can't fly it is very dangerous. (Though they abandon the young one as soon they can fly)

Migrating for better Climate:

Some of the species fly away to sustain the temperature and come back when it is suitable for them. So, Northern birds migrate to tropical places for the winter and come back to north for the summer to lay eggs.



There are too many other theories for bird migration. It had been confirmed that migration is often due to genetics than any other reason.

Further Reading: THEORIES OF BIRD MIGRATION

Sources:

[1] http://birding.about.com/od/birdbehavior/a/Why-Birds-Migrate.htm

[2] http://en.wikipedia.org/wiki/Bird_migration