A strawberry is not an actual berry, but a banana is.
By technical definition, a berry is a fleshy fruit produced from a single seed. The strawberry, however has its dry, yellow "seeds" on the outside (each of which is actually considered a separate fruit). True berries, such as blueberries and cranberries have seeds inside. However, the banana fruit is a berry for the same reason strawberries are not.
There is a theory that strawberries were named by 19th century children who picked the fruit, strung them on grass straws, and sold them as "Straws of berries".