back in the days of innocent youth, it was a popular pastime for children (especially boys) to collect birds eggs. Some boys would have vast collections from the various species of birds which inhabited their particular locale.
Once collected, only the shells were kept, these were labelled and placed in their collection box and so the process of extracting the contents of the egg began.

A small hole was punched in each end of the egg usually with the point of their compasses (remember them?) and you then had to suck one end briefly to get it started. the egg was then turned round and blown from the other end. Voila! one empty shell.

A lot of novices who had recently started egg collecting were unaware of the sucking process required and frequently had to ask for help from someone more experienced. Hence the phrase.