Bananas Are Berries and Strawberries Are Not

Botanically, a banana counts as a berry and a strawberry does not.
To a botanist, a true berry grows from one flower with one ovary and holds its seeds inside the flesh. Bananas, grapes and even tomatoes qualify. A strawberry grows from a swollen flower base, with its real fruits being the tiny seed-like dots on the outside.
Check it yourself
Search a botany text or a university extension site for the term accessory fruit, then compare it with the definition of a berry.