I hear this thrown around a lot, but to the best I can discern, it is simply unfounded. Uber and Lyft seem to pay between $1-$2 a mile. There are sites where you can put in the model and year of your car and get real life depreciation figures. Unless you're ubering around in a McLaren, you're just not depreciating at a higher rate than what Uber pays.

Prius, probably the most common ride sharing car, has a total cost, including fuel, depreciation, and maintenance, of about $0.39 cents per mile.