Why do high level/professional junglers seem to 'kite'?

One of the main reasons why they keep moving (and i do this as well) is to stay active. If you stay active while doing jungle creeps, you are trying to keep your focus on the game and are ready for anything that might happen (which most of the time is a kill attempt).

I don't think they do it for skillshot avoidance: If you keep moving, that might also mean you move into the skillshot.

For mitigating damage, the actual kiting after the first attack has almost no effect on your hp. (Note: I play a lot more Dota 2 at the moment [Eep!], where both skillshot avoidance and damage mitigation from jungle creeps can be important and is used more)

Lastly, All of these small things just add up to min-maxing of your time and staying active. Go into jungle camp, keep moving while attacking minions, find your next destination and get to the best position to move there, all the while you are staying active with the game.
(I'm still kinda new to SE, so tell me if i messed something up)

EDIT: I can't find the thread where a pro player mentioned they keep using the move command to keep active with the game, i can check later again. There are however some other threads about it. On the other side of the spectrum, your question was asked on the Dota reddit as well and got the same answers as on the LoL forums etc.
I can't link more than two things at the moment appearantly, so i kept the most important ones

Apart from keeping up your apm or awareness, usually when a camp in Jungle has two or more minions, one would move in a way that you minimize the damage taken from your primary target until the cooldown of your skill is done. For example, at the wolf camp, I will try to hit the smaller wolves first with a skill while moving to the right to make the large wolf run a bit before hitting me (and it also allows me to get use my skill again with one less autoattack from the large wolf). That makes a small difference comparing to starting at dead center of the wolf camp. Additionally, there can be enemy blind skill shots fired into the camp in attempt to steal your farm, so moving the neutral minions a little can help with that too.

My answer will focus on your title instead of your question-body as they ask two different questions.

You kite jungle creeps for the same reason that you kite champions: To minimize damage taken while still dealing damage.

For specific junglers, leashing / kiting the creeps is vital to how you'll do in your jungle. Santorin talks about Nidalee jungle clear (0-40sec):

Krugs for AD & Support:

Kiting the jungle-creeps can be very championspecific. Spells which apply Nidalee Marks (Q-Spear and W-Trap) will cause the monster to freeze. Before the W-Trap nerf you would put out a nest of traps and then kite the monsters through them almost completely avoiding damage. For updated info on how to kite with a specific champion I would simply watch an all-jungler stream. E.g Meteos or Nightblue.

For melee junglers it does not matter as the range of the monsters is big enough to hit them anyway. Range however, works a bit differently.

Ranged junglers can kite monsters around to take reduced damage. Jinx, vayne and kalista are all squishy and have no sustain but they can jungle because they can kite the monsters around slightly which allows them to stay alive. Not moving with these champions will get you killed (early).

Last patch (5.19) the way camps reset got reworked. Now it's possible to kite a camp around without having to let yourself get hit to make sure the camp does not reset. Gromp's range got reduced as well so with ranged junglers you can slightly kite him around.

Jungle monsters have a hitbox and you can use that to your advantage. Look at the raptops for instance. The big one is ranged but the 3 smaller ones are all melee. If you don't move you allow all raptors to hit you. If you move around however, the small raptors will walk in each others way trying to get to you which in turn reduces the damage they can deal.

From what I know, its for keeping their 'kiting' skill sharp by practicing on the jungle minion since they're not laning, else player who mainly jungle will have poor kiting skill and that may affect outcome of team battle if they're not used to 'kiting' skill.