It wouldn't be any different.
"Life is hard, get used to it" is a carry over from the ancient times when, believe it or not, life was fucking hard. You never knew if you were going to survive. A person, if healthy and lucky, could live to 80 like we can today, but more often were killed by disease or war or crime or starvation or dehydration or died while young... Any number of other causes, seeing life expectancy in the 20s in early stone age, and not really rising above the 40s until around the 17th century. Life was hard, and you had to fight to survive.
These days, a lot of people are unable to comprehend that, much like many have ceased to be able to comprehend the horrors of war. Its been so long since we've had to actually fight to survive, that we think that the very idea of that is stupid - there is more than enough food; look at the supermarkets! There is more than enough electricity; look at first world nations. There is more than enough resources everywhere for everyone, so life shouldn't be hard, it should be easy, those in power [Men in this case apparently] just want to hoard it to themselves. They can't comprehend how hard it is to get all this stuff, and how much harder it has been for so long in the past.
While they'd espouse being more empathetic, people like this often to me seem less empathetic, less understanding of the world, and have views purely formed from their relatively sheltered lifestyle, which they believe is just the normal state of things and if it isn't somewhere, someone must be trying to make that not happen. This isn't the case. The world struggles to produce and transport enough resources for everywhere. One of the biggest resource requirements is manpower and time, which are quite limited really. While these people will talk about how the poor should get free food, they don't want to run a farm to produce food for the poor - and if they did they would want to be paid for it, rather than just doing it for free - and if the government paid them for it they'd complain about having to pay taxes to the government, not really understanding that this is an issue faced by 7 billion people on the Earth where we have limited resources, and everyone wants a share, and if we were to equally share them then most of the people I find espousing this view wouldn't be very happy, because they'd be living in a shared house with another 2-3 families with small living quarters, eating small meals each day with little variety, having very limited time to shower or bathe or wash items, limited luxuries, and all round probably a similar life to the lives of those they say deserve more due to equality, but where they ignore the billions suffering in even worse conditions elsewhere. This is before we get into environmentalism and the fact half would probably also demand we stop deforestation, and then complain when food just disappeared as we couldn't grow enough, or we couldn't build enough houses due to lacking paper.
Life is hard, and people to some extent do need to get used to it. That said, things like environmentalism and poverty are things we should still strive to deal with, to save our planet, and our people - but that's not something that has been achievable for a long time, especially not both together, and even today it'd be a hard struggle to get there. There are some real issues, but we don't have the ability yet to solve them, and often rather than becoming an engineer, or a scientists, and trying to solve them by advancing the technology we have to solve these problems, people like this in my experience simply demand other people solve them now, because they know they can be solved its just people being greedy as to why they aren't. Naturally, not everyone is like this, and many understand how things are and simply want some aspects to change. But anyone who believes inequality wouldn't exist were women in power isn't one of those people. It would still exist. Exactly who was unequal is all that would likely change.
Now, resource issues are separate from social issues, and yes, those are things that shouldn't be just gotten used to and that do need to change. They're also not something that would be different in a female-lead society. They'd exist, its just females would be favoured by them instead of males. The fact of the matter is that gender/sex is irrelevant in terms of how equal someone sees everyone else as. That's culture, which is quite often heavily influenced by history and superstition. Conquests wars and human trafficking would have still influenced racism, as would superstitions, as would language and cultural barriers. The roles that women played and men played way back in the stone ages would still have influenced the roles they had in the modern age, and sexism and those sorts of things.
Society would look different, that is true. It wouldn't be any more equal in any way though. Hell, you want one thing that proves that it doesn't solve equality issues; "If women lead society". Automatically we're putting women in an unequal position where they are above men, and are preferentially given more roles. In this society, the thought "Lets make them more equal" couldn't exist, because then it wouldn't be a women-lead society, but an egalitarian society. Saying that its a matriarchal society already discounts the equality argument. Its not equal. And that kind of instantly defeats the entire point that they're trying to make.
