Usage of 'on the brink of'?

Question

(Talking about a chimp): "In human age, he would have been on the brink of puberty." I was told that this sentence is odd because 'be on the brink of' is usually used for something negative: suicides, disasters etc. Though this is most often the case, I don't think this is necessarily true. For example, you can say "on the brink of greatness". In this particular sentence, would it be sound more natural, comparatively speaking, to use "on the threshold of puberty" instead? -Edit- Google Ngram Viewer makes it clear, I think: http://goo.gl/IqozD

Answer 1

It refers to on the edge or on the starting point