Why is a satellite in orbit considered to be accelerating?

According to Newton's Second Law, the satellite is accelerating because it experiences a net force acting on it, and also because its velocity is changing. It is also useful to know that the force of gravity provides the necessary centripetal force for a stable orbit.

a satellite is acted upon by the force of gravity and this force does accelerate it towards the Earth. In the absence of gravity a satellite would move in a straight line path tangent to the Earth. In the absence of any forces whatsoever, an object in motion (such as a satellite) would continue in motion with the same speed and in the same direction. This is the law of inertia. The force of gravity acts upon a high speed satellite to deviate its trajectory from a straight-line inertial path. Indeed, a satellite is accelerating towards the Earth due to the force of gravity.