A Very Fine Swan
The topic of self-esteem is rather a popular one these days, and certainly an awful lot of populist academia is based on the idea of low self-esteem being at the root of poor classroom achievement or disruptive behaviour (which doesn't quite gel with those very bright, gentle kids who have zero esteem but expend themselves in study rather than causing mayhem... and yes I speak from both personal and professional experience).
Does disliking yourself prevent you from giving or receiving love, attaining career success, being profoundly artistic or creative? No. Many immensely talented and successful people have struggled with depression and self-hatred, many people who wouldn't give themselves the time of day will nonetheless love and care deeply for others. Granted their lives are not necessarily as happy as they could be, but their lives are far from thwarted. There's also some research to suggest that very high self esteem is actually associated with aggressive, antisocial behaviour (so it's not a cure-all!)
Where does our sense of value come from? Initially from other people, from our nearest (and theoretically dearest) who let us know if we are important to them or just a bloody nuisance that gets in the way, or even something far worse than that. Unplanned children invariably necessitate the parents having to reassess their lives and change their plans ~ for some the joy of parenthood may outweigh whatever dreams have been shelved, for others the child may become the focus of resentment (and children are very quick at picking up on such cues, even if the parent is careful never to outright say that they would have preferred to be free to do other things).
However, let's not get all Freudian and trapped in the parent-child dynamic, because children are surrounded by extended family, other kids, the growing circle of adults that they come into contact with on a regular basis. All these people can potentially impact a child's sense of worth for good or ill. It's not just a matter of raising or lowering esteem, but also shaping our perceived sources of worth for the future ~ is it our intellect, beauty, sports prowess, helpfulness, artistic talents etc. that get praised (or belittled)? It's surprising how little people change over the course of decades in terms of what they derive their sense of worth from. The sensible person strives to expand their range of sources, rather than have all their eggs in one basket, and we may well argue that there are certain crucial stages in life where the sources of personal worth are reviewed. Referring back to the Duckling story, puberty is an obvious example where we both start to value other people for different traits (their sexual desirability etc.) and start to reassess our own worth in the light of those same traits. Both genders experiment with different looks, changing clothes and hair and body shape to see what makes them most desirable... which returns us to the notion that we can only know desirability through the lens of another's eye. Someone else has to tell us that we have become a swan (though equally we have to believe them and credit them as a valid source).
In my own lifetime I think it has become more acceptable for young men to take care of their appearance, and the sight of scruffy great slobs expecting women (or men) to reciprocate their sweaty pawings merely because of the bulge in their wallets has become relatively rare. Indeed, I've heard some women complaining about the vanity of their metrosexual boyfriends or husbands. Yet the reliance on sexual desirability as a source of worth still seems curiously female in our culture ~ it's common to compliment women for looking attractive, but comparatively rare to flatter men in that way. In a similar way hearing women fretting over the perceived loss of their looks and resenting younger rivals is unremarkable, whilst men who worry about the loss of their charms or who find themselves dumped for a younger, hunkier model are rare enough to be figures of fun. For older men financial status still seems to be the primary source of personal worth. Whether that's a good or bad thing is probably open to debate.
I've no idea if Hans Christian Andersen ever read the Irish myth of Oengus mac Og, the god of love who becomes a swan, but there's an interesting echo between the children's story and the myth with the choice of the bird to represent sexual awakening and maturity. Regardless of whether we are male or female, almost everyone wants to feel themselves to be a swan at some point in their life. I don't consider this to be a sign of patriarchal oppression or any such thing, but a normal expression of human nature and the wish to feel that one still has worth in the eyes of a current or prospective sexual partner. I'm sure there's a kernal for a story in there somewhere!