The two great elemental schemes of the hand agree about the index finger and about nothing else. In the esoteric Buddhism recorded in Japanese sculpture the digits are the five elements counted inward from the little finger: earth, water, fire, then wind, fu, at the index, then space at the thumb. In the yogic hasta mudras the assignment differs at four digits out of five, with fire at the thumb, ether at the middle finger, earth at the ring and water at the little, but the index is air, vayu, which is the same element under another name. Two systems built on different cosmologies in different centuries put moving air on the same finger.
It is also the finger the commonest hand seal uses. Touching the tip of the index to the tip of the thumb, with the other three extended, makes the gesture of knowledge, and it is so widely reproduced that it is the picture most people have of a mudra at all. Read through the elemental scheme it joins air to fire, or wind to space, depending which list is in use. Read through the anatomy it is simply the easiest contact the hand can make, because the thumb opposes and the index is the digit it opposes most directly.
The pointing use is older than either scheme and belongs to no tradition in particular. What the schemes add is a claim about what the finger is made of, and there the agreement between them is worth noticing precisely because it is the exception.
Sources Mudra: A Study of Symbolic Gestures in Japanese Buddhist SculptureE. Dale Saunders with Asana Pranayama Mudra BandhaSwami Satyananda Saraswati