Why do children, Brownies age, need a 'safe space' from boys?
For my Brownies, our safe girl-only space allows them to take the lead in all activities, obviously, but they notice it most when it comes to STEM-based & physical activities that they're not being pushed aside by their male peers as happens [sometimes literally] in other contexts. At Brownies they don't ever hear "NameOfThing isn't for girls"/"girls can't do NameOfThing" or similar versions of the gender-stereotyped nonsense that's used to exclude & put them down elsewhere - very much the reverse, in fact: we actively remind them that they can like/wear any colours & play with any toys & women can do any jobs [that they are qualified for] & at their age they're just as physically strong & fast as boys are - & they'll always be as clever as they are. Because they are, sadly, being told otherwise elsewhere.
My Brownies who play football for a local team find themselves excluded from games at playtime "because girls can't play football". We have to play an adapted version in meetings for safety reasons related to the design of our hall, but play we do. One wee girl's even being told by the boys in her class that she's "not allowed" to support a men's football team because she's a girl - we've reassured her on that & she's feeling happier knowing her Sixer has been to lots of a local premiership team's matches.
The Brownies get interrupted & talked over in class by male classmates. When we discuss things at Brownies that doesn't happen - they take turns to speak; they know that I'll get to them; & on the VERY rare occasions anyone talks out of turn (usually when we're discussing plans for the term & there are Excited Squeakings/a couple of Brownies are Suddenly Inspired & want to add something to their Six's suggestion list) I remind them they've to be quiet & listen to the person who's speaking. My Unit regularly has Brownies arrive who'll not speak at all in any discussions (I'll keep track of who's spoken & ask Brownies who haven't if they've any ideas etc), will barely answer the register even, and after just a term they'll start talking; by the time they leave they're leading discussions with their Six.
When we've had girls either transfer in from Cubs or do both Brownies & Cubs, we've been told Brownies lets them do activities they wouldn't get to at Cubs (like craft & drama) & that the atmosphere is much calmer. I realise the stereotype is that Brownies do craft while Cubs are off hiking etc, & in some areas Cub Units provide more opportunities for physical activities than Brownie ones (it should be said that Scouting has an infrastructure that supports this) but my Unit makes a very real effort to ensure that we provide opportunities to Have Adventures Outside. We've no outdoor space other than a (locked) car park (with multiple hazards) where we meet, so we hold meetings in local parks/on the Heath/at the nature reserve. We play hide & seek in the dark, we bug-hunt, pond-dip & climb trees. We've provided opportunities for the Brownies to try climbing & sailing & indoor caving & zorbing. Spending a day doing the Circus Performer badge last summer was pretty full-on physical too. When we do these things, there are no boys there to push them out of the way &/or tell them they can't do it or they're doing it wrong or they're rubbish at it. Obviously not all boys do that - but it's behaviour all my Brownies experience from their peers. Although Ban Bossy is US-based, the idea holds true in the UK too. Have a look at Girlguiding's most recent Girls' Attitudes Survey to see how pervasive gender stereotypes are even at Brownie age - can you not see why girls would benefit from a space of their own where those ideas can more easily be challenged? You can access earlier surveys if you scroll down the page - they're interesting reading, if somewhat depressing at times.
Some girls, of course, need a space away from boys for faith reasons, the obvious group being Muslim girls. It is also the case for some of the Jewish population - when I was at university I spent a day during one of the holidays volunteering at an event for refugees with a Leader from a Jewish Unit who was fascinated by my Catholic Brownies & Guides (it's possible I was the first Catholic she'd met tbh) & membership of Girlguiding allowed girls & young women in her community to try new things & gain new skills - but their participation was possible only because Girlguiding's a single-sex organisation.
Very sadly, given the rise in cases of that kind, we will almost certainly have some young members who need a space away from boys due to a history of [sexual] abuse by their male peers.
The point, however, of a "safe girl-only space" isn't vilifying boys or suggesting their presence automatically makes a space unsafe. The point is the positive impact of homosociality & that girls are known to benefit hugely from it; & the "safety" of the space is a reference both to allowing girls to be themselves without fear of judgement/censure; & to the fact that they are protected from harm by the way Girlguiding is run.