If you live on the south of the planet, your longest and shortest days are just the opposite.

Notice how the earth is tilted.
As it goes around the sun throughout the year, the top of the planet gets more sun at one time of year (summer) and less at the opposite time of year (winter).

Until the summer solstice, the daylight lasts longer and longer each day.
After the summer solstice the daylight gets shorter and shorter each day until the winter solstice when daylight is the shortest and starts getting longer again.