Me me abnormally large (note that this could also be interpreted as above average in size, or large relative to surrounded or other clumps of matter that could be put into the same category as the one in question) homosapien in possession of XY chromosomes which produces male gametes, or sex cells, commonly known as sperm. A homosapien with XY chromosomes is generally larger in height and stature than a homosapien of the same gene pool with XX chromosomes. This is amplified by the homosapien being referred to as 'big'. This imposes an image into the mind of other homosapiens of a intimidating organism, presumably with extreme physical prowess. This could help the homosapien avoid conflict by threatening any opposing homosapiens, and also attract a mate, due to homosapiens possessing a XX chromosome generally being attracted to more powerful mates, for protection, and an improved gene pool.
As you can see, this call of 'me me big boy' at first seems strange, but there is an extremely logical evolutionary reason behind it. The call can help the homosapien prosper, find a mate, and avoid potentially harmful conflict.