So that we have a place to start --
Arthur, a colleague recently brought up the story of Columbus' egg, often quoted as an example of creativity (and since you mention eggs...). Here's the Wikipedia quote of the 16th c. "source":

Columbus was dining with many Spanish nobles when one of them said: 'Sir Christopher, even if your lordship had not discovered the Indies, there would have been, here in Spain which is a country abundant with great men knowledgeable in cosmography and literature, one who would have started a similar adventure with the same result.' Columbus did not respond to these words but asked for a whole egg to be brought to him. He placed it on the table and said: 'My lords, I will lay a wager with any of you that you are unable to make this egg stand on its end like I will do without any kind of help or aid.' They all tried without success and when the egg returned to Columbus, he tapped it gently on the table breaking it slightly and, with this, the egg stood on its end. All those present were confounded and understood what he meant: that once the feat has been done, anyone knows how to do it.

Now when I heard this story, I found it very unsatisfying as an answer. Crushing the tip to make it stand upright? As with the Gordian knot, it is not exactly a clever solution; it is one of violence, even if also if genius.  As you say, Arthur, violence is sometimes necessary for creativity, so I'm not speaking against violence per se; but it does limit the scope of the imagination.

Afterwards I wondered how I would have solved it.  I can give you at least one non-violent way to make an egg stand upright: wait about two weeks and place it in a bowl of water; the air pocket inside will have come to the top and the egg will balance upright.

To see whether this is helpful in answering your question, we should ask:
Is it correct to say my method is non-violent?
It does not destroy the shell, but it does use a certain amount of time.

Going back then, Arthur, to what you ask. First of all, I agree that one should be careful to distinguish history from nature. Women have traditionally had much less power and thus less of the luxury of wanton destruction -- or of the authority for it. Still, they have managed to operate creatively even within very narrow bounds; to take a random list of examples of "women's work" from "traditional culture" and "history" (take these words with a lot of salt):

-- creating human beings in their bodies,
-- cooking; remember that historically many nutrients were not bioavailable unless long and complicated heating, fermenting, or other processes were invented/discovered; 
-- creating themselves as works of art; the muse, the salon hostess, the royal mistress, the actress;
-- creating worlds, in many traditions essentially singlehandedly representing the weight (sometimes burden) of culture and "mother-tongue"
-- writing; in the last three hundred years, undisputably great novels, essays, poems...

This is a tiny sample and an enormous question, but so that we have somewhere to begin, let me observe that these all have in common a certain creation in time, as opposed to creation in space (which we might call the realm of violence). 
When one works in time the violence is always either ahead of or behind you: what has been superceded, what has been prevented. In this realm of the invisible, the deep creativity comes when something arises -- a certain force of life -- which we don't understand instantaneously, just as we don't experience a human being all at once but rather as someone who unfolds through time; and the corresponding "violence" is that to create in this way, and to know in this way, requires the proper use of time -- ultimately, one pays with one's life.
Perhaps men and women pay a different price, but it is a heavy price nonetheless...

Here too, Arthur, when you speak of "women artists" we should be careful to distinguish between the arts: women have, historically, done great things in literature, in music, in theater (arguably the arts which make masterful use of time), more so than in architecture, sculpture, painting (with notable exceptions).

To associate destruction with creation in relation to art is kind of a romantic, bittersweet notion. The reason there aren't as many female artists that are considered great is because women were(and still aren't, to some degree) not encouraged to be creative. Little boys and males in general are encouraged to use their imaginations much more. Female children are more encouraged to just focus on clothes and dolls and other petty superficialities that their mothers probably focus on. Adult females are encouraged to do detail work that doesn't allow for as much creativity, such as office work, whereas men go on to become inventors and corporate trend-setters. I'm not sure why, actually, but I've just noticed that women are NOT encouraged to be creative like men are. They are just encouraged to like "nice" things, "pretty" things.  Women are actually kind of raised to be small-minded and weak still, which is not conducive to great art.  (Women give their power away to males, and because many focus so much on details, we can't see this!) But nevertheless destruction does not have to be incorporated always into art-at least, not in a morbid way. To do so is to become to hung up on the darkness inherant in our world. I didn't always think this way though... By the way, I'm a female.

Young boys are encouraged by their mothers and fathers to be destructive. The reason they are ACTUALLY so destructive is because they are not given a healthy outlet to express their emotions. If a little boy gets hurt, the father maintains a stiff upper lip and tells him to grin and bear it, that the pain will pass. If a girl gets hurt, both parents will carry her off and fuss over her. Young boys are crammed into pigeon-holes at a young age. They are not allowed to like "girly" things or express their feelings. They are taught to like rough things, because people just assume that's how little boys are when in fact it is part of their conditioning by adults so that they will fit the male stereotype when they get older. So young boys feel this great confusion because they cannot express themselves and are, from birth, strictly inhibited. This manifests in destructive behavior because they can't express their feelings in words. Unfortunately, mothers play a heavy hand in this because they just shrug and perhaps even encourage their male children to be destructive, smiling while saying, "Boys will be boys!" Ironically, it is the Mother that should be teaching her male child(especially)sensitivity and respect for life. That is why so many men grow up to be womanizers and that is why so many men remain destructive well into old age, with their destructive tendencies manifesting in the corporate world. Their mothers never teach them sensitivity and respect. Their mothers just shrug and say,"Boys will be boys!"

In reality, men have the capacity to be just as sensitive and nurturing as women, while women have just as much capacity to be creative and to lead. Both sexes are kind of inhibited and polarized though.

  When building block towers, when the last block is in place the only step forward is the destruction of the tower to clear the way for a new tower. Destroying mom's china cabinet is a cry for help. I think this is true irrespective of sex. DADA is a poor example or perhaps I'm alone in thinking that drawing with magic marker  on a copy of the Mona Lisa or a plumbing fixture is neither destructive nor art.
  One winter, while taking a navigation course at a local high school, I had occasion to use a cubicle in the boys washroom. Among the grafiti liberally covering the walls were numerous references to various individuals who apparently were available to actively or passively engage in sexual acts of a nature unknown to me until I was middle-aged. The lives of these individuals must have been hell during the school day. They must have been thankful that they were not females who, you say, are uniquely destructive in their use of cruel words.
  On my small island there is a saturday market during the summer; mainly for the tourists. It's an 'arts and crafts' market that is divided with few exceptions by sex. The guys do whirly-gigs and wooden bowls and rustic furniture. Crafts if you will. The women do a little of everything but other than food it is all useless stuff. Paintings, calligraphy, fabric wallhangings, assemblies of found things, art in all its forms. I like the baking. Pleasing to look at and even better to eat. My point is that the only truly creative people here are the women. I guess all the guy artists are just too successful to live here. But that's okay because there is pleasure in these uncreative artists. I wouldn't trade them for a museum of DADA art.
  I'd like to offer a story told to me by my elder. It's about male and female roles in life.
  One fall day my elder was  home quietly playing on the back deck. He was alone with his mother. His sisters were off with friends. Dad was away very early that morning, before sunup, with friends on a weekend moose hunt. He had wanted to go hunting with the men but was too young and had been left at home with the women.They lived in Canada's far north and to go on a moose hunt was just a matter of driving a few miles to get far enough from the houses so stray bullets were not a danger. My elder's mother came out the back door carrying dad's 22 rifle they used for shooting pests like ravens and scaring deer out of the garden and signed for him to be quiet and follow her. They went to the bottom of the yard where a berm separated the yard from the shore of a stream that flowed past. Carefully he and his mother peered over the berm and there was a moose. From the kitchen window his mother had seen the moose rack tossing up and down as the animal grazed on the far side of the berm. She carefully slid the gun onto the berm, sighted, and dropped the moose where it stood with a brain shot. That sunday night my elder listened enthralled as his father and his friends, home from an unsuccessful hunt, feasted on fresh moose liver and onions and potatoes and told tall tales of successful hunts they had had. His mother was in the kitchen, tired from a hard weekend butchering hundreds of pounds of moose, doing her woman's work washing dishes but humming as she worked.