The list is a bit short sighted:
1. Doctor
Why it's everlasting: While humans pride themselves on being the most intelligent of species, we still have a mortality rate, and we still get bumped, bruised and diseased along the way. We will always need people to investigate and treat our medical conditions.
If you can't make an AI that is better at reading an X-Ray than my doctor we need to restart computer science from the beginning.
2. Teacher
Why it's everlasting: There will always be a need for education, and there will always be a need for people to do the educating.
We invented books to handle the learnign part. The keeping little monsters out of the way of real people until the turn 18 could be handled by robots with laser beams.
3. Mortician
Why it's everlasting: Unless a solution for mortality is found and available to everyone, there will always be a need for someone to care after the deceased.
Two words - Soylent green.
4. Waste Disposal Manager
Why it's everlasting: Humans create a lot of waste, biologically and otherwise. We'll always need people to maintain and relocate our messes.
You put out a consitently shaped bin in the same place at the same time. Add an RFID tag and an autonomous vehicle picks it up.
5. Scientist
Why it's everlasting: Humans will always ponder our surroundings and how everything works. We need people to dedicate their lives to the cause and effects of our actions and our environments to deal with changes.
Of course - they are in charge of inventing the robots.
6. Tax Collector
Why it's everlasting: As the old saying goes, "In this world nothing is certain but death and taxes." For all reported income, there will always be a form of collection to aid government programs.
Everyone is paid electronically, everyone buys goods electronically. A person is needed to track this why?
7. Barber
Why it's everlasting: People will always need to have their hair cut and groomed.
Probably true - personal services is going to last a lot longer than other jobs.
8. Soldier
Why it's everlasting: Even if world peace were a reality, there would still be a fear of future wars based on history.
Combination of remote operated vehicles and outsourcing to 3rd world mercenaries.
9. Religious Leader
Why it's everlasting: As people continue to ponder the meaning of their own existence, a majority find a need for people to assist them with a form of spiritual guidance.
You mean TV evangelsists aren't CGI ?
10. Law Enforcement Officer
Why it's everlasting: If we are dependent upon a system that governs, we will also be dependent upon people to enforce the rules of that system.
Probably I imagine the interference from the Taser could be a problem for a robot. Plus it's tricky to make a machien that runs on donuts!
11. Farmer
Why it's everlasting: One of the basic human needs is food and, even though farming is increasingly consolidated, there will still be a need for someone to grow it.
Two words - toaster pockets.
Did you see the 'inkjet' concrete printer that could produce a home direct from CAD?
