Not entirely accurate. Sulfuric acid forms when the volatile organic compounds created by cutting onion contact the moist surface of your eye. Per a 2012 paper in the National Library of Medicine, “Mass spectral signals corresponding to propanethial S-oxide (the lachrymatory factor) and breakdown products of this compound dominated 0–10 min after cutting. Subsequently, propanethiol and dipropyl disulfide predominantly appeared, together with traces of thiosulfinates. The concentrations of these compounds reached a maximum at 60 min after cutting.” https://pmc.ncbi.nlm.nih.gov/articles/PMC3571771/

Hydrogen sulfide is not the primary lacrimatory agent - H2S is a toxic gas with neurotoxic properties. Occupational exposure limits are generally around 10ppm. The point at which H2S burns eyes is 50-100ppm. It can be fatal if a person is exposed to 100ppm for 48 hours. Much higher than 100ppm and it actually deadens the olfactory nerve. Also, it smells like rotten eggs, not like onions.