The evidence does not support the claim as stated. Smoking and nicotine can inhibit aromatase activity and lower estrogen in women, but that is not the same as causing aromatase deficiency, which is a rare genetic disorder caused by CYP19A1 mutations. The claim conflates temporary enzyme inhibition with a distinct inherited medical condition.
Caveats
Do not confuse reversible aromatase inhibition from nicotine or smoke exposure with the clinical diagnosis 'aromatase deficiency.'
Most supporting studies show short-term or in vitro enzyme suppression, not that smoking causes a permanent deficiency syndrome.
The wording overstates the evidence by using a specific genetic-disease term for a pharmacologic effect.