My EG4 3000W inverter provides a 125A DC breaker to the Lifepower4 battery. The battery also has an on off switch breaker of 100A. Why do I need to install the 125A CB when there is one on the input to the battery already, isn't that redundant?
Because you might have more than one battery installed. If you e.g. have two, you can easily provide more than 125A to the inverter while not coming close to 100A per battery.