Hi OP if it's any consolation I think the only child spoilt stereotype is a complete myth. Being spoilt depends on the wider family circumstances not on how many brothers/sisters a child has got. In any case, what does spoilt actually mean? It seems such an imprecise word to me.
I've known only children who've had REALLY tough upbringings - i.e. in one case - not enough food to eat - this is in a developed country - the UK. How on earth could he be spoilt? We have a benefits system in this country to make sure that even children from the poorest families eat reasonably adequately. He didn't have enough food because he had a neglectful, feckless mother. I also know another only child - severely beaten by his father. Again - how is this spoilt? Any one using this erroneous stereotype is imo emotionally immature and is deliberately trying to bring another person down as well as being narrow minded. Another only child was brought up by an abusive, neglectful, alcoholic mother. Spoilt? I don't think so.
To look at this from another angle, if we were to take this 'spoilt' argument to it's logical conclusion you could argue that the vast majority of people are ' spoilt' in the UK compared to average people in developing/third countries as we have much better health care, a much better standard of living - we don't have to walk 10 miles barefoot every day to get clean water!!
About the not sharing argument - all children learn to share soon enough in school/nursery. Also, in an affluent country now like the UK, siblings usually have their own toys etc anyway, and don't have to share - especially so with siblings with a bigger age gap whose would need very different 'toys' and forms of entertainment.
I read a very good book on this subject which confirmed that the negative only child stereotypes are a TOTAL myth - the only thing which only children MAY be more likely to be affected by and this is very much JUST a maybe - is that they are the only ones 'told off' in that particular family situation - so this in SOME circumstances may effect them negatively -(not, I don't think if parents are broadminded and rational).
The only other thing that this book alluded to is that because only children don't have anyone who 'knows' their parents exactly like they do - it takes them longer to realise that their parents may be 'getting it wrong' in some areas. Again, only a maybe, and it may not affect them negatively anyway.
I also think that only children are perhaps, more likely to have to deal with difficult family situations on their own at some point - but, far from being a negative thing, this could give them confidence.!! So for example, an only child can walk into a room where they don't know anyone, think 'well, I'm an only child, I've coped with difficult situations on my own - this social gathering should be a breeze' and have the confidence to walk up to someone and break the ice!!
Hope this helps!!