We're guessing that even if you have dainty portion sizes, not every morsel you put on patrons' plates is eaten.  And you probably discard produce that has gone bad from time to time, as well as trimmings from both animal products and produce.  All of those items can have a useful future ahead, but not if you send them to a landfill!

Composting completes the cycle between farm and table that starts with good soil growing healthy crops, then moves to consumption of those crops, and then should end with excess food being composted to enrich the soil for more crop growth. 

If food waste ends up in a landfill, it will remain largely intact for a very long time.  Due to the high degree of containment in a modern landfill (good for water supplies), biodegradable materials will...well, they won't biodegrade.  The absence of light and oxygen stunts the breakdown process to the point that the landfill preserves biodegradable stuff quite well.