Infant's Swimming and the Spirits
Linked to the spiritual idea of water and the souls of the dead, in Daijo and some parts of Feng-Young the ability of a baby to 'swim' is thought to determine its relatinship with the spirits.
Summary
The essential idea is that most babes are capable of holding their breath and 'swimming' when placed in water, but some babes are not. In actually the babies are simply holding their breath and doing the motions, but do not have the strength to swim. Since bodies of water are meant to house the spirits of the dead, both malicious and benevolent, the ability of a baby to 'swim' when placed in water was meant to signify they were more favoured by the spirits, and had less to fear from waterways and were less likely to be targeted by tricks. Of course, the opposite is also thought to be true; babies that cannot do this are spurned by the spirits for some reason and should take precautions to protect themselves from the spirits. Many families with a child who didn't display these instincts moved far away from any bodies of water.
Historical Basis
The simple fact of the matter is that children and babies often drown if they get into the water, and with the existing belief about water holding spirits it is not surprising that they made the logical connection between that and a baby that drowned almost immediately and one that survived long enough to be rescued.
Cultural Reception
For the most part, families react to having a 'spurned' child more with protectiveness than anything, easily making them the coddled child of a family and sometimes going to extreme measures such as moving far away in an effort to protect them. There have been instances, however, of families giving their children up or leaving them for dead in the belief that the spirits hate them for a reason and they're touched by evil somehow. This is generally frowned upon, however, and it is believed that for whatever dark karma they rid themselves of by abandoning their child, it is paid back to them for engaging in such a selfish act.