I'm no expert in general relativity, so please bear with any misconceptions in my understanding :)
In general relativity, Einstein showed that we experience gravity because standing on earth is actually being in a non-inertial (accelerating) frame of reference in a curved space-time.
Only free falling along a geodesic contoured by the curvature of the local space-time is considered an inertial frame of reference.
On the other hand, we are led to believe that Newton's second law: $F=ma$ is valid only when one is in an inertial frame of reference.
So shouldn't $F=ma$ be invalid in most use cases classical mechanics (obviously it is valid, but what am I missing)?