An inertial reference frame is one in which a particle has constant velocity if and only if has a zero net force acting on it.
How can one determine if a given reference frame is inertial? For example, consider an elevator falling on earth, uniformly accelerating towards the ground. There is a man inside and can see only the interior of the elevator. If he throws a ball horizontaly w.r.t to the floor of the elevator, he will observe the ball moving in a straight line, as the ball has the same vertical acceleration w.r.t to the Earth as the elevator.
If we now place this elevator in the far reaches of the solar system sufficiently far from any planets and we repeat the experiment, the man again observes the ball moving in a straight line.
The problem is, in the first situation, the frame of reference of the man is accelerating with respect to the earth, and there is a real force acting on the ball. In the second situation there is no force acting on ball, but the behavior is the same.
The man has no way of knowing if there is a real force acting on the ball, so he can't determine whether his frame of reference is inertial, right?