why does it make a difference what species it is
The whole point of mentioning that a 'human' baby is less cognitively developed than mature animals of other species, is to call into question the basis on which we protect a particular life. Singer postures that the grounds for protecting life is based on it's measured abilities, this is a rational basis for valueing adult human life, your abilities are what make someone a whole 'person', and objectively valuable.
If a particular human has lesser abilities than a particular animal, why should possession of a certain DNA sequence count for more than superior intellect and capacity for suffering?
That is the crux of Singers argument:
"it needs to be shown why mere membership of a given biological species should be a sufficient basis for a right to life. "
http://www.utilitarian.net/singer/by/1995----03.htm