I dont think its "sexist" at all
(though horrified at sound of those stitches... ouch)
It must be medically better for baby and mum for mum to not have GA if possible. The baby needs to be considered too.
Can imagine a teenager might really hate the idea of people doing stuff to his willy while he was awake. He can recover from GA in his own time, and not be needed to care for and breast feed a baby over the next few days.
My Dads male friend had a GA for an operation on his eye-ball. He just could not cope with idea of watching the Dr insert a needle into his eye-ball while he was awake. They suggested a local, so it was not been medically necessary to have a GA, but he was allowed. (not sure i could be still and not blink while someone poked a needle into my eye ball either, ewwwww).
I have had a fair few GA's in my time. They completley knock me out for a few days, and make me very sick. I now have learnt to always ask for anti sickness drugs before a GA, which stop me being sick, but no idea if thats safe for baby or for breast feeding,? and even if it is safe it must be better to not have if avoidable.
Even many big operations can be done under local aneasthetic.... think of elderly patients where a GA is likely to kill them but they need an operation. (my great uncle, who sadly passed away last year, had quite a few quite big operations with just local, before he died.... if thats possible then you can back track the arguement to "why do women who are just having a few stitches down there, need a general?"
Just to add, have not (yet) had any stitches down there, but am pg and i cant for a moment think that having stitches is nice at all. I cant yet imagine how horrid it must be, and while i really have no issues /fears about the giving birth, its the episiotomy / tearing / stitches part that freaks me out the most.