How does one truly get white socks white? Mine get dirty and I wash them with detergent and bleach, but I find they only get gray with time, and the dirt stains I get along the non-shoe covered areas never come out, so I have pairs of socks with brown rings just above the ankles. Is there something I’m missing, or are clean white socks a myth? 
You can try using a lot more bleach, try using oxygen bleach, try presoaking them in dishwasher detergent, try using Mrs. Stewart’s Blueing, or buy new socks.
How much bleach can one use before it starts becoming detrimental to the fabric? I understand if you use too much it will turn things yellow?
Never messed with blueing before. Heck, don’t know what you’re supposed to do with it. I’ve only ever seen it used as a Colombo plot point.
Next time, don’t buy black socks.
For blueing, the instructions are on the label. Basically, you just add a little bit during the rinse process, when your washing machine is full of water. It’s just blue dye. Small amounts will make the greyish or yellowish fabric look white.
Ah, chemistry. 
Thanks.
90 degree wash with a cup of oxy biological powder and a cup of thick (not thin) bleach in the machine.
Keep in mind that for cotton socks, the original white color is fake. They’re dyed that way to look cleaner. So the more you wash them, the more that dye will wash out. And if you’ve been sweating in the socks and leaving the sweat there, the bacteria will permanently change the fabric. You can’t fix that any more than you can undigest food.
You referring to that Oxy-clean stuff, or some other oxy substance?
Do you have hard water? That can affect how your detergent works.
Don’t believe so. I’m not noticing build up in the sinks and tub. More of never having been taught the finer points of doing laundry.
Thank you, thank you for asking this question.
I have a water softener.
I bleach my whites (maybe 1/2 cup bleach in with the whites once a month)
Wash on hot/warm
My damn socks (like yours) are never white. Always a dull gray. They’re white when I buy them; but if I wear them once with any sort of colored shoe they pick that up. Gray, brown, blue. Doesn’t matter.
I’m still looking for an answer, though I may try bluing.
More bleach is unattractive to me, as “hotel” levels of bleach irritate my skin to all hell.
Ancient Chinese Secret…
Sorry couldn’t help it.
I solved the problem by buying… BLACK SOCKS. 
A pre-soak with bleach should help somewhat, but like others have said, that ship might just have sailed (it’s awfully hard to get t-shirt underarm stains out, too). While we’re sharing laundry tips, I’ve found that nothing takes grease stains out of clothes like a pre-treatment with dishwashing soap - squirt a little right on the grease stain, rub it into the fabric, and wash in hot or warm water.
Then I’ll have to start a thread on why my blacks are turning gray.
Second the recommendation of bluing for turning dingy socks whiter, but it’s not going to remove dirt rings. My understanding, however, is that once you’ve dried stained clothing, you’ve set the stain and it will never come out. The only think left to do is bleach it to within an inch of its life and then buy new socks.
Black socks with shorts and sneakers looks really silly, though. Better stick with neutral colors like tans and greys. It looks a little less silly than black or stained socks.
How long do you wear your socks before washing?
I think my water has a lot to do with it. I have the same problem as the OP and all my clothes look dingy. I never had this problem when I didn’t live in Chicago. I’ve tried everything from bleach to water softners, to blueing and nothing working. They still are dingy.
I personally have never found anything to make a dingy clothing item come back to life. But that is probably just me. I really think it’s just the watger or the pipes in Chicago, 'cause when I lived in the suburbs or in another state, I never had this problem
Only once. I try to avoid generating a ‘do not enter’ zone of funk around myself.
ETA: Found some laundry bluing. Gonna give it a try tonight!
A half cup of bleach per load is hardly anything if you’re trying to bleach them whiter. Try washing them in a much stronger bleack solution and see what happens.
Wear gloves; it dribbles and stains your hands.