This issue is NOT a duplicate of MC-129085 ! It is about merely holding the item not swapping to it.

When riding a pig with a carrot on a stick in hand and falling, the pig’s FallDistance maxes out to around 3.7613 after 4 blocks of falling, and never increases beyond this. Teleporting the pig also does nothing while holding the carrot on a stick.

It also behaves erratically under 4 blocks of fall, generally being half as much as it should be. Expected behavior (FallDistance increasing by 1 every block of free fall) is resumed when not holding the carrot on a stick, or switching to another item mid fall.

This is particularly annoying to test, because of the second aforementioned issue, thus to reproduce the bug you must make stairs and lead the pig up the stairs. Then, create a dummy objective called “FallDistance”, run this command every tick, and set that objective to display on the sidebar :

/execute as @e[type=pig, distance=0..1, limit=1] store result @s FallDistance run data get entity @s FallDistance

By varying the final “scale” argument (omitted in example), you can get an better idea of the exact value where FallDamage stops updating.