Melonade's points are good ones although some women do travel alone. I've stayed on a pacific island alone a few times in my 40s, days though not weeks. I've gone abroad for work to places like Iran and Lagos, again in my 40s leaving children at home, not that I am a great fan actually of business travel (and that is nothing to do with sexism, just the waste of time and tiredness although it does let you see other cultures - eg women in full black burkhas on Kish island beach whilst the men are free in their speedos).
Sexism differs in different countries. Much of Africa thinks it's fine to beat your wife for example. We tend not to get that in the UK. Much of South America has very macho men (although a good few female Presidents) and women spending a fortune on plastic surgery. China has quite a few female entrepreneurs but with India kills many many baby girls a year before birth simply because they are female.
The original item was about women in the media, how girls are shown that what counts as a girl is if you've had your nails done and ironed your hair rather than can you lead a major organisation or perform heart surgery and I do agree it is pretty bad in the UK.
On melonade's point about older women (of which presumably I will be one soon going into my 50s, although I work full time and am fairly successful so I tend to get the more work, admiration, wisdom of age thing which is nice) that is certainly an issue in professions like the media but also teaching. One of the teaching unions has been talking this week about needing to consider women teachers in the menopause who once it is over have at least another 10 years of good work ahead of them.
We also have no culture of revering the old in the UK. Instead we either feel sorry for them or they are the butt of jokes from the young which is awful. We tend not to keep them about us nor live with them and we shunt them into homes to be shut away a bit like people did with disabled children in the old days, whereas those older people have a lot of knowledge. I suspect this will change now we have no compulsory retirement age although some women may well nto have jobs if they find it hard to get back into work after children which could make things even worse as men may well be working from age 50 - 75 and earning and being visible and enjoying a job and some women who find it harder to get back into work (the ones who take career breaks) will be even further marginalised and also short of money and in a sense hidden at home.