Why do we say that objects moving in a circle have acceleration even if their speed remains constant?

Because their speed might remain constant, but their velocity doesn't. Remember, velocity is a vector, so it has magnitude (which is the speed of the object), but also direction. For an object moving in a circle (or along any curve, for that matter), the direction of the velocity is constantly changing. This change in the velocity vector is explained by an acceleration pointing towards the centre of the circle called centripetal acceleration.