"However wouldn't an electromagnetic rail launcher system work better and give a faster launch velocity?"

A rail launcher might work on the moon where there is no atmosphere, but on earth such a system would fire the projectile (like a cannon or supergun) with maximum speed coming out of the muzzle where the air is the most dense, near the ground. The projectile would slow down a lot before it achieved a significant altitude and since it has to achieve orbit velocity, that means it is going faster than orbit velocity near the ground -- it would probably burn up. Rockets actually launch vertically in order to get above the atmosphere. Then when the rocket clears the atmosphere it leans over and propels the payload horizontally and really picks up alot of speed. It can go faster once it is above the atmosphere. With my Skyhook idea, the tether rotates as it orbits so that when the tip of the tether comes into contact with the atmosphere it has almost no horizontal velocity relative to the ground -- so there is minimal air resistance.

"I don't mean to be critical but what would happen if the tether broke, lets say with the star ship in the Earth direction?"

The tether releases payloads at 7900 km altitude, and payloads are carried by their extra momentum to over 12,000 km altitude. So the starship would probably be orbiting at least 12,000 km above the Earth. If the tether broke it wouldn't affect anything orbiting that high.