Why aren't the antibodies in the mother's milk digested by the infant's digestive system?
Demers-Mathieu et al. 1 used ELISA to quantify immunoglobulin concentrations from milk after 2 hours of digestion in the stomachs of preterm-delivered and term-delivered infants.  From the abstract:

Total IgA concentration decreased by 60% from human milk to the preterm infant stomach and decreased by 48% in the term infant stomach. Total IgM and IgG concentrations decreased by 33% and 77%, respectively, from human milk to the term infant stomach but were stable in the preterm infant stomach.

The authors note that the infants enrolled in this study had a variety of medical conditions, but &quot;no overt gastrointestinal tract issues or other medical conditions that have been associated with an effect on gastric emptying or digestion capacity.&quot; Two hours of digestion was chosen to ensure recovery of sample from the stomach while maximizing digestion time, per the gastric emptying times observed in Siegel et al. 2
So, it appears that term infants are digesting antibodies from their mothers, but a substantial portion of immunoglobulins remain intact.  Weaver et al. 3 report IgA concentrations between 0.311 and 1.247 g/L across 1600 breast milk samples, with negative correlations to maternal age and parity.
Taking the median IgA concentration of 0.708 g/L, a 48% reduction gives 0.368 g/L post-digestion.  Dewey et al. 4 report that 3 month-old infants consume 818 mL of breast milk (assuming 1 g/mL) per day, on average, which suggests that ~300 mg IgA are available to the infant intestine from daily breast milk consumption.  If the adult human gut produces 40 to 60 mg IgA per kg body weight per day 5, then ~300 mg IgA is in the ballpark of what a 6 kg infant would need to phenocopy IgA concentration in the adult gut, assuming limited immunoglobulin production by infants themselves.
So, it seems like hypothesis #2 is close to the truth, at least for highly abundant antibodies like immunoglobulins:

Antibodies are present in such large amounts that many of them are undigested by chance.



Demers-Mathieu V, Underwood MA, Beverly RL, Nielsen SD, Dallas DC. Comparison of Human Milk Immunoglobulin Survival during Gastric Digestion between Preterm and Term Infants. Nutrients. 2018 May 17;10(5):631.
Siegel M, Lebenthal E, Topper W, Krantz B, Li PK. Gastric emptying in prematures of isocaloric feedings with differing osmolalities. Pediatr Res. 1982;16(2):141-147.
Weaver LT, Arthur HM, Bunn JE, Thomas JE. Human milk IgA concentrations during the first year of lactation. Arch Dis Child. 1998 Mar;78(3):235-9.
Dewey KG, Heinig MJ, Nommsen LA, Lonnerdal B. Maternal versus infant factors related to breast milk intake and residual milk volume: the DARLING study. Pediatrics. 1991;87(6):829-837.
Jacob Campbell, James Berry, Yu Liang. Chapter 71 - Anatomy and Physiology of the Small Intestine, Editor: Charles J. Yeo, Shackelford's Surgery of the Alimentary Tract (Eighth Edition). [via ScienceDirect]