Think of 'wear down' as a slow process, not something that happens suddenly or quickly. Walking every day will gradually wear down your shoes.
Pro Tip 2/3
Physical Objects
'Wear down' often applies to the physical degradation of objects over time. The statue wore down after centuries of exposure to the elements.
Pro Tip 3/3
Gradual Change
Use 'wear down' when you want to express a gradual reduction or change, rather than an abrupt one. The river slowly wore down the rocks into smooth pebbles.