Among the six fu, the Small Intestine is paired with the Heart in the Fire phase, which is the least intuitive pairing in the whole scheme and one the tradition does not much explain. The channels connect and the phase requires a yang partner for the Heart; that is most of the argument.
The function assigned to the organ is stated in a single phrase that recurs throughout the classical literature: it separates the pure from the impure. It receives what the Stomach has broken down, sends the usable portion onward for the Spleen to transform and distribute, and passes the residue to the Large Intestine and the Bladder. Because the same phrase serves for a mental operation as well as a bodily one, the classics extend the organ's remit to discernment, to the sorting of what is worth keeping from what is not.
That double use is characteristic. Chinese medicine does not maintain separate vocabularies for physical and mental function, and the atlas records the fact rather than resolving it, since the ambiguity is in the sources and not in the translation.
The western scheme places the intestines under Virgo, treated separately. Neither account is an anatomical claim about the small intestine and neither is clinical guidance.