Self-employment tax liability is based on your having $400 or more "net self-employment income", which is 92.35% (to account for the deduction for one-half of SE tax) of your *net* Schedule C (or C-EZ) income. If your business deductions brought your net Schedule C income below $433.13 (92.35% of which is $400), you do not owe SE tax.
Uber itself isn't a small business; YOU are the small business. Uber (as well as Lyft and nearly all other ride-sharing companies) treats most of its drivers as independent contractors, meaning you get 1099-MISC forms and file as a self-employed person on Schedule C; if you have enough income, you also pay SE tax on Schedule SE.
