The ability of men and women to enjoy flowers in Japan is definitely something to do with the artistic nature of the culture. Elegance, refinement and delicacy are all themes you'll find in Japanese artwork (as well as efficiency and minimalism) and flowers are considered to have a lot of these traits. Most human cultures love flowers. Use petals and flowers to beautify things. The Japanese though, spent a long time in cultural isolation developing their arts and crafts and appreciation of art to a fine point. Go pretty much anywhere in Japan even today and you can sense a tangible "reverence" for beauty and good skilful art everywhere you look.
The aversion guys have elsewhere often for liking "anything floral" is probably due to a desire to separate the sexes in terms of behavior... there was a distinct advantage for people who were "identifiable" as male or female most of the time, through the history of our species. If you were not identifiable - i.e. visually androgynous - this meant you were an unknown quantity and unknown quantities posed potential risks to primitive people. This is more than likely why women don't like being confused for men and vice versa in most situations. Because of the behavioral and role divide (biological) between men and women, it was dangerous to be confused with a man if you were a woman (more likely to get hurt for example), and it would probably not help you climb the ladder in the world of men to be confused for a woman. Neither sex benefited from acting like the other when subject to the general rules of survival. This continues from our most distant ancestry right up till the present day. If you asked a cis female friend if she'd like to be taken for mannish, or a male friend if he'd like to be mistaken for a woman the answer would probably be a vehement no. They might not be able to explain precisely why, but something buried in the brain and our behavior tells most people it's "wrong". For any strong negative impulse in a person, you can assume that behind it probably had something to do with our ancestors' most primal needs for survival. Not least in the case of people, for looking/acting like one sex or the other in order to reproduce.
Trans people are outliers in this regard, and yet we still have similar strengths of feeling and negativity towards feeling "wrong", either by going against mainstream culture, or going against our own internal feelings. Going against our "tribe" or culture was a dangerous thing, and still is sometimes. Hence, most people tend to keep strictly to gender expectations in public. Flowers became something it's accepted for women to like in most of the world, but not for men because men were policed by both men and women to be raised to shun feminine characteristics and adopt masculine ones. This was done for survival purposes, because back in the day men needed to be robust and not particularly sensitive in order to defend others. Society tended to disallow men feminine activities in order to keep them in this mode. There was danger in adopting feminine behaviors as a male, and you would run the risk of being policed for it.
There will be some who will want to call that "patriarchy" or some other nonsense but it's simply a biological fact that men are the ones our species can most efficiently put in harm's way to defend the physically weaker members of it, women and children. To put women and children in harms way instead of men, or put them in harms way along with the men is illogical. So men were raised to be tougher and to act differently from women and children. They were not encouraged to engage in feminine behaviors like enjoying flowers. Even now you'll find most womens' "ideal man" is not a guy who enjoys "behaving like a woman", even if it's a horribly stereotypical attitude to take.
I have no particular feelings about this, whether it's good or bad, this is simply the way nature has shaped and moulded our species. The absolute origin of all of this behavior and role modification is that nature saw fit to divide roles for reproduction. Females put far more investment into young, and males less. As a result the males began to take on the role of being defenders and fighters, because they were free to and it made sense... and females took on the role of being the core of a tribe raising the offspring. You can see it in most of our closest animal relatives like monkeys and of course any mammal is subject to this division of reproductive labour. Almost all male vertebrates are free from immediate reproductive burdens and instead have thrust on them the dangerous burden of fighting to get a mate and/or defending those mates. Almost all female vertebrates had to modify their strategies for dealing with their particular burden as well, which was also dangerous.
Almost all of our behaviors and physiological difference have come about from this most basic division of labour. Women knew strong men could provide for and defend them better so they selected stronger rather than weaker and smaller men as mates. After millions of years, the modern human man and woman look the way they do because of this. And women still tend to prefer masculine men, and men tend to prefer feminine women. Not all of course but the statistics in studies bear it out.
Thankfully most modern culture allows people a bit more breathing room these days. Unless it's islam which still doesn't allow men to wear decorative jewellery, or for the sexes to overtly behave like one another, etc. and there are a few others. But given all the modern accomplishments we have, men and women are still very different and because of that biological fact that women carry children and men do not, probably always will be. For there to be a major shift we'd have to evolve beyond needing women to carry children to term, perhaps by use of machines, and genetic experimentation. Which I'm not particularly comfortable with since we don't really have a clue about what we'd be doing to ourselves. (But if anyone's going to do this it's China. They're already genetically engineering giant animals etc. so who knows).
