Common question, but you don't have to worry.
Assumption 1: A battery can have "too much" discharge current rating.
The battery will
only deliver the current that the load requires. You could have a battery capable of providing 10 trillion amps of discharge current, but if the load is pulling 1 amp, the battery will only deliver 1 amp. Of course, that size battery will likely be fairly large and heavy.
Assumption 2: The controller will "pull" a maximum of 120A.
The controller is rated to be able to
pass 120A continuously. But in reality, 120A
continuously will heat up the ESC quite fast and drain a 5000mAh battery in 2.5 minutes flat. The ESC is actually is able to pass current bursts in the
hundreds of amps
very briefly. The ESC does
not limit the current by any means - other than bursting into a ball of flame if current is too high for too long. That 120A figure is just a ballpark value to give you an idea of how to compare it against other ESCs.
Anyway, the battery voltage,
motor, and the
mechanical load placed on it is what determines how much current the ESC will have to handle. The controller doesn't pull the current, the motor does; the ESC just regulates (via your throttle finger) how much battery voltage is actually getting to the motor.