Please note: this answer has been revised with recent information that seems to be indisputably canonical given the sources.
Tricia Helfer, the actor who played six, answered this same question on a Reddit AMA. She says:
It was a mercy killing. Six was fascinated with seeing the innocence
of the baby (holding one for the first time) and knew that the bombs
were going to go off soon, so chose to end the baby's life quickly and
painlessly rather than having it suffer during the bombing.
In the podcasts, Ronald D. Moore explains that early on, there was uncertainty about how much of the Cylon culture would be revealed. He considered having the Cylons being just a relentless, faceless, threat, much as they were depicted in the episode 33. So, initially, there was much more of a ruthlessness built into the Cylons as a culture.
However, as the story evolved, it went in the direction we saw, which was that the Cylons were rapidly evolving a culture that has more in common with human culture, including disagreements among Cylons about the ethics of wiping out humans, and whether or not humans were merely vermin or equals.
Additionally, Ronald D. Moore has also said:
Well, not to give anything away here, but the scene demonstrates both
the cold-blooded nature of the Cylons and their more human aspect at
the same time. Watch Tricia's performance carefully in this scene and
I think you'll see that from her point of view, she's conducting a
mercy killing -- as frightening as that may be to you or I.
So comments below make sense, here is the text of the original answer that has been superceded by the actor's and director's explanations:
I believe that the reason that particular Six model snapped the baby's neck was because the humanoid Cylons were a relatively new step in evolution for the Cylons at that point. And she was certainly very new to being in a human society.
She was, in a sense, somewhat sociopathic, not having worked out human emotions, appropriate behaviour, and so on. My interpretation of the motive of snapping the neck is that she was seeing what it would be like to do so, but it could be argued that it was for other reasons, equally lacking in empathy.
As the series goes on, though, she learns more about humans, about society, and about herself, and so she develops a more nuanced and sympathetic understanding of ethics and of living among both humans and Cylons.