Karṇavedha
The popular claimThe piercing of the ears is the shortest saṁskāra in the list, and the one whose reason the texts give most plainly.
Not every one of the sixteen was in every list. Karṇavedha appears in the later enumerations — Vyāsa's sixteen includes it — and its textual base is thinner than the others. That thinness is itself informative: it entered the list because it was already universal practice, and the list caught up.
What the texts give
The rite is short. The child is seated facing east; the father or the surgeon pierces the right ear first for a boy and the left first for a girl, with a needle of gold, silver or iron according to the family's means, and a verse is said to the effect that the child may hear well and long. A thread or a fine ring is passed through. That is the whole of it. Kātyāyana gives it in a few sentences; Pāraskara's school in a few more; neither has a fire.
Suśruta's reason
What makes Karṇavedha unusual is that the medical literature claims it directly. The Suśruta Saṁhitā, in the sixteenth chapter of its Sūtra-sthāna, describes the piercing of a child's ears in the sixth, seventh or eighth month — earlier than the sūtras — and gives its purpose as protection from disease and as ornament, rakṣā-bhūṣaṇa-nimittam. It then describes the technique: the child held in the lap, the lobe transilluminated to find the natural point, the needle for a soft lobe and the awl for a thick one, the wick left in the wound, the oil to dress it, and the faults of a bad piercing.
Whatever one makes of the protective claim, the passage is a surgical description, and it shows a rite and a medical procedure that were, for once, the same act. The saṁskāra list absorbed something the physicians had been doing.
Timing
The muhūrta treatises give the day: the sixth, seventh, eighth or twelfth month, or the third, fifth or seventh year; the Sun in Uttarāyaṇa; a nakṣatra from the gentle group — Mṛgaśira, Puṣya, Hasta, Citrā, Anurādhā, Śravaṇa, Dhaniṣṭhā, Revatī, the Uttarās, Punarvasu; a weekday other than Tuesday, Saturday or, for some, Sunday; a fixed or dual rising sign; the child's birth month avoided. Nothing is said about the tithi beyond the general exclusions. It is often folded into the same day as the mundan.
The order of the ears
The right ear first for a boy, the left for a girl, is the one detail every source agrees on, and it is worth noticing that it is a rule about sequence rather than about which: both ears are pierced. The gendered order is old and is followed in most families still; where it is not followed, nothing in the texts says what would follow from that, because the texts do not attach an outcome to it.
What survived
Everything. Karṇavedha is probably the most universally performed saṁskāra in the list, because its result is visible, permanent and ornamental, and because the medical tradition and the family tradition agreed on it. The verse has mostly gone; the goldsmith or the piercing gun has replaced the surgeon; the maternal uncle often holds the child, as at the mundan. Some families keep it as a rite with a small pūjā first. Most keep it as a visit to the jeweller. The texts would recognise both.
What this page does not say
It does not say that piercing on the wrong day or in the wrong ear first has a consequence, and it does not endorse Suśruta's claim of protection, which is a claim about medicine from a text two thousand years old and should be read as such. The rite is a piercing and a verse. That is what is here.
Source — Katyayana Sutra (Karnavedha section) and the Paraskara tradition on the rite; Sushruta Samhita, Sutra-sthana 16, on ear-piercing in the sixth to eighth month; Muhurta Chintamani on the timing conditions
Every claim on this site names its source, and every calculator shows its arithmetic.