Even Dove stings my eyes, albeit not as much as actual soap soap. Then again, even the earliest version of Johnson's Baby Shampoo stung my eyes a little, although it was an improvement in that regard over soap, which is all I had before baby shampoo came out.
OK, by now you know from other posts that you're trying to compare your soap to something that's only soaplike and doesn't even exist in liquid form. (Dove has an amount of stearic acid which would be hard to incorporate into a liquid; their liquid products are formulated differently still.) So the eye sting is not an indication of anything that "went wrong" in your liquid soap. But if you're interested in making a low eye sting liquid, albeit not an actual soap soap, we can advise you about that.
BTW, Dove does (and AFAIK always did) have
some actual soap soap in it, but that's not its main cleaning & lathering ingredient.
As to your question, why use [actual soap] soap, there are many reasons -- many of which, however, apply less to liquid products than to solids. Specifically why do hobbyists make soap as opposed to other detergents? Basically it's because soap is the only detergent that's easy enough to make for most hobbyists
out of something that's a different chemical substance. There are plenty of hobbyists who make other detergent products for washing skin & hair, but what practically all of them (I'm allowing the possibility it's not 100%) do is just mixing ingredients, not transforming them chemically. Of course, the same can be said of melt & pour soap making and of hobbyist lotion making, bath fizzie making, etc. I only mixed the ingredients for my liquid bubble mixture, for instance, even though I'm a biochemist.
The reason for this is that saponification is a relatively easy thing to do. The precursor ingredients to soap are esters, and esters break down easily. And once they've broken these esters (mostly triglyceride) down, most hobbyists would not want to do a "workup" as is usually done after a reaction in organic chemistry to separate the products. Rather, they keep all the products in the bar of soap (or liquid soap) that results: the fatty acid salt that chemists now mean by "soap", most of the water that was used, the glycerin that's also liberated from the glycerides, and the unsaponifiables which come thru from the fats & oils unreacted and contribute to the emollient properties of the product, not to mention superfatting. Other than making soap, the only other surfactants I can fairly easily see a few hobbyists trying to synthesize would be some of the sugar esters, and even those would be considerably harder than making soap. I have considered doing the mild-conditions sulfonation, using sulfites, required for the sulfosuccinate esters my bubble bath calls for. The analogous process for most other surfactants requiring sulfonation would call for sulfuric or even fuming sulfuric acid!
Interestingly enough, one of the closest things to saponification of triglycerides is transesterification, which is a step in making some other surfactants, but was also done by hobbyists with waste cooking fats during the biodiesel fuel fad a few years ago. Instead of water, it requires methyl alcohol, also with lye, but the process requires workup to remove impurities and to assure dryness.
