In my 2012 SX there is no "sport" mode. You just turn on ECO, or turn off ECO. But you can make your own sport mode:
Engage manual shifting mode (hit the paddle shifter, or hit the stick shift to the left to put it in manual mode
Smash the gas peddle and DON'T shift anything.
The car will ride the current gear as long as possible, until automatically upshifting when the revs are at max. It's a very fun way to drive the car. But I usually prefer to just stay in ECO.
Also, your car will learn your driving styles and adjust the shift points based on those driving patterns. If you really don't like how the car is shifting in any mode (ECO, or Normal, or Sport), maybe you can reset the learning so it goes back to default.
The issue would be that you drive aggressively in ECO mode, so the car learns to undo the ECO stuff. Or, you drive very conservatively in Sport mode, so the car is less aggressive. I'm still foggy on the details of the shift learning, can anyone chime in on more details of how the car learns to customize the shifting based on your driving history?
Personally I try to turn off ECO mode before I do aggressive driving.