When a rancher wrangles a critter, his next job logically should be to pick up said critter and take it to it's drop off point.
However, wrangling a critter and moving it to a drop-off point are two different chores, so in order to have this happen, you have to set priorities to make this happen.
The issue is that even with priorities properly set, this doesn't happen. A rancher will wrangle a critter, then do ANY OTHER chore, regardless of priorities.
After they have completed said chore, if the priority is set properly, they will come back, pick up the wrangled critter and move it to the drop-off point.
This leads me to conclude that their list of 'todo' things isn't updated after they complete a task, and before the game determines what chore is next on the list, but later than that, thus causing this behaviour.
This can lead to serious inefficiency for said dupes, especially once bases start becoming larger, and even lead to having to rewrangle critters because of this.
( For instance, you order your rancher to wrangle a drecko somewhere at prio 7, and have a drecko drop-off set to prio 9, but also have a hatch ranch with a grooming station at say 6. This rancher will go wrangle it, because this is his highest priority, after which he will go off and groom some hatch, before coming back to pick up the drecko and moving it to the drop-off. In a larger base, this can cause a serious delay between wrangling and moving, even more if downtime happens while they're busy with the other chore, or are on their way again to move the drecko, thus delaying it even more, which can lead to the critter breaking out of it's wrangle who-knows-where. )
Steps to Reproduce
set up critter drop-off wrangle a critter
This issue has not been confirmed by a developer yet.