A strawberry isn't an actual berry, but a banana is.

 

Strawberries are not berries. They actually are an example of an “aggregate fruit”, forming from a flower that has many ovaries; the ovary being the part of the flower that eventually develops and ripens into a fruit. Once the ovaries are pollinated, the ovaries will swell and eventually form the strawberry as we think of it.
As noted, strawberries form from a flower that has many ovaries. This makes them a complex fruit, much like blackberries or raspberries. Actual berries, though, are what are known as “simple fruits”, meaning they form from a flower that has only one ovary, such as grapes.
Bonus Facts:

• Examples of actual berries that most people don’t think of as such include: bananas, tomatoes, and watermelons.
• The garden strawberry was first bred in France in 1840 by crossing a Gragaria virginiana, from North America, with a Gradaria chiloensis, from Chile. The former was noted for its great flavor and the latter was known for its large size.
• Strawberry plants are rarely propagated by seeds anymore; rather, they are generally propagated by cutting off runners from existing plants.

Expand for References:

• Berry
• Are strawberries berries?
• Garden Strawberry
• Aggregate Fruit