system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5:Why can a manual car with a dead battery be started by pushing it but not an automatic?
gpt
Most people have seen a movie where someone needs to start an old airplane so they walk up to the propeller and someone gives it a mighty spin.  This is enough to get the engine "going" and it starts.  It's basically the exact same thing that's happening when you start a lawn mower by pulling on the cord.

Most engines, once running have enough power to keep running.  But getting going requires more power than the engine has initially.  Basically an engine has it's lowest power when it's very low in the RPM range, such as when the engine is initially starting.  But an engine is like an avalanche or a cascade, once it's going it stays going but starting it going requires some kind of energy.

Lawn mowers use a pull cord to get the engine rotating and then once it starts firing it has enough power to keep going.  Old airplanes needed someone to come manually spin the prop, old cars used a crank in the front.

Modern car use an electrical motor called the starter.

Now, lets get to your question directly.  With a manual car, as long as it's in gear if you spin the tires it will cause the engine to spin.  This is the opposite of normal operations where spinning the engine causes the tires to spin.  But with a manual car it works in both directions.  So pushing the car (rotating the tires) will cause the engine to rotate and if you go fast enough it can be enough for the car to start and keep going on it's own power. 

Automatic cars work very differently.  In a manual car there's a clutch that disconnects the engine and drive wheels so that you can shift gears.  But as long as you are not activating the clutch there's an actual mechanical link between the wheels and the engine.  This is why, in a manual car, when you come to a full stop you must engage the clutch or the engine will also stop. 

An automatic car is much more complicated but lets simplify things and just say that there's no mechanical link between the wheels and the engine.  The torque converter is basically a fluid linkage. Think of it like 2 fans spinning in a thick liquid.  One fan spins, this causes the liquid to spin and this causes the second fan to start spinning. 2 fans encased in liquid. This allows automatic cars to shift gears without needing to activate a clutch, it's also what allows automatic cars to come to a complete stop without stalling the engine. But it also means that a bump start just won't ever work. Since there's no direct physical linkage spinning one fan very slowly won't get enough of the liquid moving to ever cause the other fan to spin.  So doing a push start just won't ever work on an automatic.