I think the main reason no one knows how to sew a button is that they don't NEED to, generally speaking. Mass-produced clothing isn't the same quality it used to be; it's cheaply made, rarely has buttons (when was the last time you saw someone under 40 wearing a buttoned shirt or dress?) and by the time someone loses a button, the item of clothing is already falling apart and so a replacement is purchased.
Back to my previous
Brave New World reference, I don't think it's as much that the clothes now can't be repaired but that we, as a society, have developed the attitude that we shouldn't bother mending things when we can just buy a new, inexpensive replacement items.
I've lost buttons and had tears develop in the seams of several inexpensive pieces of clothing, something I've attributed to the lower standard of quality you refer to. However, by fixing the item, rather than simply throwing it away, I've prolonged the usefulness of the items. These will likely never be items that last a lifetime ... but they will last much longer than their first failure.
This is something I've been challenged with for other things too. How often to I replace or throw out items that only require minor repairs or a little elbow-grease to remain useful?
For example, my kid's rabbit ate through his laptop charger's power cord so my first reaction was to buy a new one. They were pretty pricey so I made him wait while I shopped around and he ended up not being able to use his laptop for quite a while as I vacillated on what the best option was. In the end, after fixing something else with a similar problem, I just fixed the cord and he was back up and running. But why wasn't my first reaction to fix it? Why was I so eager to spend money on a replacement with out even considering repair as an option?