Would be interesting to learn more about the role of women in Russian history.
Russia differs from women in Europe and the Northern Americas, Australia, etc. in that they were handed 'equal rights' by the Soviet regime, which didn't necessarily give them access to the upper echelons of power, it just put them out doing hard labor. They just had to go to work like men did, even fighting in wars as snipers and so forth. They didn't have a long struggle for basic human rights, the right to vote, the right to equal pay for equal work, like women in the west. By all accounts I've read though, Russian still lags far behind the west in fair compensation, women earning 60% to 40% of a man for the same work.
Women in Russia do get the longest paid maternity anywhere in the world though, but if the wage is not a living wage, it may not be that beneficial, and may cause employers to not want to hire young women who can leave for over a year on full pay.
Seems like there is a breakdown in general Russian society due to the many wars which killed off many men, leaving a surplus of women in some areas, and men who just didn't want to participate in family life, problems with alcoholism and so forth. It's not clear to me what exactly is going on with Russian men, but it is clear that many Russian women look for men outside of Russia to find a suitable husband for raising a family to the point that it has become cliche. A lot of women are also trafficked by the Russian mafia and other groups from that part of the world because women are looking to escape crushing poverty, and end up in slavery.
Urban women, like elsewhere in developed or developing countries are probably similar in that they have figured out they don't need the hassle of an alcoholic abusive husband, and can be quite fulfilled by working and living how they choose. They've figured out that they have to work, but then they have to go home and work again. They carry a double burden. Maybe a lot of women are deciding that don't want the double burden.
Russia has a declining net population, so that may be part of what Patriarch Kiril is trying to address. Also, abortion is widely and easily available in Russia, and is often used as a form of birth control rather than as a last resort since it is so cheap. People who are already in poverty don't necessarily want to add children to the mix, or if they are moderately comfortable, they may not want many children. Women can't be out being good little communist workers driving trucks and building railroads when they have a passle of kids to take care of as well. And Soviet collective daycare didn't always work out so well.
Other concerns the Patriarch Kiril could address are the high levels of alcoholism, and educating people about alcohol use during pregnancy. From what I've heard, Russians don't even consider beer to be alcohol, but as a food. I recently heard of someone drinking beer during the fast, and others were confused, thinking that abstention from alcohol is part of the fast. Apparently not in the Russian tradition, which made sense to me if they really classify beer as food.
So, it's not clear to me why Patriarch Kiril would just choose one aspect of modern Russian society on which to comment when there are obviously many other problems he could address as well, if that is indeed what happened.
Could be the western press just picked up on the one part of what he said because it goes against sensibility.