Of course it's conditioning. I won't have a go btw as I shave, not for cleanliness but comfort (I get long thick hairs that stab me and have had ingrowing hairs in the past which suck, despite washing etc the only thing that stopped them was shaving).
I don't shave my legs, armpits or other areas though. But i do think I would look better if I did.
The idea that we look better without hair, are cleaner without hair etc comes from social conditioning, it's true.
It's conditioning that both sexes receive in some ways
eg men feeling they can't have long hair, nor do anything "feminine" like work in midwifery or hair dressing, men in nursery settings being treated as a Paedo. My ex was a nursery worker and several women would not put their children in his care or questioned him about his career choice 
discrimination and conditioning is everywhere.
For men, to do something feminine is bad. To work in a feminine industry, shave your legs (I know a man who does this as he doesn't like the feel of his hairs, fair enough, he's ripped to shreds over it If wearing shorts), staying at home is both admirable and seen as under the thumb at the same time (if you're single, it's admirable you're stepping up because your ex is probably crazy, a cunt or dead. If you're in a relationship you're under the thumb and a sissy and you should've worked harder and told her to stay home
)
For women, to do something that doesn't involve staying at home, taking your husbands name, giving your child your husbands name, staying married (no one wants to be a feckless single mum, do they? Praise the single dads though! What champs!)... is bad.
Your natural wrinkles and grey hair will make you almost invisible.
Your body hair is bad and you should be bald from the eyebrows down...
we're all involved in these norms, big and small and they should be challenged.
But we won't get around this by being aggressive to people who believe the norm.
Talking civilly, allowing them to disagree and make up their own mind is the step forward.
I can't speak for all but someone insulting, degrading me or telling me I'm basically a mindless sheep won't make me side with them.