No form of murder is humane you dumb tool. This isn't a case of the baby had to die so lets achieve this objective in the least painful way possible. If the baby had to do then they didn't have to murder it. They could have put it up for adoption or just fucking left it a church. What did the poor kid do to deserve being strangled to death? It could have had a good life with another family.
Properly performed strangulation results in loss of consciousness quicker than you would think. I'm not saying that the young girl in question performed it correctly, as I'm sure that a 14 year old girl would have no knowledge of how to do so, but as a general rule, I would consider any form of strangulation more humane than most alternatives. She was in a bathroom, if the options are slicing the baby's throat with her father's razor, beating his head against the bathtub, drowning him or strangling him, strangulation is in my opinion the clear choice.