This is an interesting thread.. lots of people quite angry at the op.. sorry..
Overall in the UK, according to the Independent Schools Census, 49% of pupils educated privately are girls. This report makes for good reading.
www.isc.co.uk/media/7496/isc_census_2021_final.pdf
Having spoken to an ex head at a boys school that admitted girls, there was a culture of admitting girls because it was of benefit to the boys and also one of appearing to become coed while limiting the number of girls to less than 50% so as not to change the culture of the school too much.
In all coed educational settings, there is a risk of educational stereotypes being applied.. as someone up thread mentioned.. boys being lazy, boys being poorly behaved and for girls, that they do not do as well in Maths and STEM subjects.
Overall girls outperform boys, even in the STEM subjects - for the first time in 2020 a higher percentage of girls got A* in GCSE and A Level, than boys.. however, the number of girls taking maths, physics, comp science is significantly lower than the number of boys.. 43% (estimated from the graph below) of the A Level cohort sitting Maths, were female and 28% of the cohort sitting further maths were female. This is based on UK averages.
ffteducationdatalab.org.uk/2021/09/which-a-level-subjects-have-the-best-and-worst-gender-balance/
If STEM subjects are important to your daughter, how does your school of choice fair on this metric?
We are surrounded by ingrained sexism and I see it in many areas. At primary school it was houses all named after famous white men, invited authors being male (despite the number of female authors outnumbering males ones), unequal allocation of access to sporting facilities for girls. At secondary school, it was unconscious bias in the classroom... putting introverted high performing girls with noisy lazy boys (yes I know - but it was admitted by the school) and not recognising that girls were showing their level of attainment in a different way to the boys.. (the higher maths class excluded girls with high grades if the teacher didn't believe them capable even though it included boys with lower grades, purely based on 'I know what it takes to achieve', what was happening was that girls who are socially conditioned not to shout out the answer were being perceived as not capable and were not being encouraged to trust in their ability). These are anecdotes but there is good research on the impact of stereotypes in the classroom.
We have a local university programme that takes high performing maths students from secondary school and gives them extra maths coaching. They have a much higher drop out rate from girls than boys and when they offer the programme divided by sex, the drop out rate for girls is significantly lower.
Someone else mentioned schools placing too much emphasis on gender - I disagree. Until every second person in the government, on every board, in every place where decisions are made - if I may be so bold as to steal those words - is female, we need to keep showing our daughters that they deserve to be there.