Joe, try thinking about this: "the default setting in life is MALE, females are 'other' " and see where that train of thought takes you.
It is pretty likely that your young female student friends have experienced sexism - but that they haven't recognised it as such yet. You see, it is just their life - they have no other frame of reference. Their female friends have all experienced similar, to them it's all just a part of life.
Here are some things that have probably affected them so far:
Judged on their attractiveness to men;
Judged on how they dress.
Bombarded with media/pop culture images of scantily clad, overtly sexualised women (eg, miley cyrus)
Probably have to brush off comments about their bodies/looks on a daily basis, or even physical assaults;
They shouldn't walk home alone at night;
They shouldn't drink too much, wear high heels, low cut tops etc, because if they are raped, they will be blamed for it;
They have to guard their drinks on a night out;
They are expected to be the gatekeepers of virtue.
When they start work and then a family - they will have to fend off interviewers suspicions that they will get pregnant and go on maternity leave, they will most likely get paid less for the same job. They will most likely have to give up their job/go part time/arrange childcare and probably, do most of the housework too. Working mothers are more likely to take the day off to look after their children when they're sick. The term 'working mothers' is commonly used/heard, 'working fathers' isn't - they're just 'men with families.' They are more likely to stagnate on their career ladder than fathers whilst bringing up a family - or be seen as selfish for pursuing a career rather than looking after their children.
And yes, the patriarchy does pitch women against women - but it's not other women that are at fault, it's patriarchal society.