The Twelve Tables, the famous early laws of the Roman Republic, don't themselves survive, so they have been partially reconstructed from references to them in Roman literature. The idea of the obligation to kill a deformed child seems to come from a reference of Cicero in his De legibus. In a discussion of political offices that arose during times of civil turmoil, Cicero has a character in his dialogue remark that after the turmoil such an institution was "quickly put to death, as hideously deformed children should be, according to the Twelve Tables." (Cicero, The Laws 3.19, trans Niall Rudd, Oxford 1998, p. 157). This passes into Warmington's reconstruction of the Twelve Tables (IV.1, Harvard 1957, p. 440-441). Unfortunately, there is no justification of why. I haven't been able to find a reference in the Digest that would provide some jurisprudential rationale. Take a look at Jane Gardener's Women in Rome, especially p. 161 n. 39. She cited Dig. 25.3.4, an excerpt of the third-century jurist Paulus, which defines abandonment and exposure of an infant as killing, without any distinction of deformity. Now this is not to say that such a distinction was not made in the original text and edited out by the jurists of the Christian Justinian who compiled the collection. Even Berger, in his Encyclopedic Dictionary of Roman Law (p. 500) , makes no mention beyond the Twelve Tables.

That said, my guess would be that even physical disability carried with it serious legal repercussions. In a predominantly oral legal culture, the deaf or mute lacked full legal agency. If the Romans also drew a connection between physical birth defects and intellectual disability (though that term itself cannot be applied to the Roman understanding of mental disorders), then even more strict limitations on agency would follow. This is just a guess of a possible reason though. not even getting into other social or cultural rationales at the time (my main area is medieval disability). Though she does not touch on this precise question, Gardener's Being a Roman Citizen has a great chapter on legal concepts of disability.