>that child gets showered with attention.

and all the other resources are poured into one child instead of being spread around several children. Thus only child has higher IQ and development level than when there are several of them.

http://www.nytimes.com/books/first/m/mckibben-one.html

"A twenty-year tracking study of 3,000 high school students demonstrated that only children have higher IQs than their peers with one sibling -- in fact, "there are marked negative effects on IQ of increasing sib size."

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There are also similar results of first child having higher IQ than second - as all the attention goes to him/her during the critical first years of brain development while second child doesn't have such undivided attention.