Over time I've become comfortable and happy picking with my thumb and index finger only, Doc Watson style. But, I started taking online lessons, and my instructor keeps insisting that I use all my fingers. I keep telling him that I'm really not interested in that, but he keeps pushing it. I know that he'd be right if I was a 14 year old just developing playing habits. Technically he's right, in every way. But, I'm an old man, and I don't have any ambition or vision of becoming an accomplished master of the Ukulele. I just want to have fun with it, and learn a few different tricks and licks.
Yes, I brought Kimo's playing to my instructor's attention. And, he couldn't quite get it either. We worked on my learning "Hallelujah" Kimo style. My instructor finally said Kimo was "hiding" what he was really doing under his hand, and more or less dismissed his style of playing. But, I really like it! And, I tried to get my instructor interested in helping me learn to play "Deep River Blues" Doc Watson style, and he produced a handwritten TAB that incorporated all the fingers. Then, he said it really couldn't be played on Ukulele the way Doc does it because of the "missing" strings. I don't believe that. I wasn't shooting for a 'note for note' imitation of Doc's version. I just wanted to learn to travis pick the tune using thumb and index finger the way Doc does it. Very frustrating!
I'm not an authority, but having had some lessons in other chordophones, the ukulele is a really informal instrument. There are what teachers call "best practices" and techniques to play the ukulele better, but I think it's all a lot less rigid than, say, guitar instruction (which, by your description, your teacher almost sounds like a guitar instructor who teaches ukulele).
As a kid, I briefly had a classical guitar teacher who couldn't really teach me what I wanted to learn, partly because it was outside his narrow expertise. Later I had a mandolin instructor who kept telling me instruments and performers I liked weren't
real mandolins and mandolin players. I didn't have these teachers for very long, and I didn't learn very much from them. I'm sure they're very proficient in their areas of expertise, but it wasn't really helpful to me.
These days there's so much material out there, it's easier to learn without direct instruction, but if you have a teacher, you should probably get one that respects your goals. Granted, there are times when students want something unrealistic. But it doesn't sound like your instructor is helping you learn what you want. If you're doing distance learning, and especially if your instructor
is primarily a guitar teacher, you might want to see if you can find another whose expertise is the ukulele. Even if his expertise is the ukulele, maybe he's just not the best fit for you?
Kimo Hussey's playing technique and style is very unique. He's a very nice man and play the ukulele mostly "his" way. If he "hides" the way he play the ukulele, he would still be a great ukulele player. That thumb and index technique belongs to Kimo. No one plays it beside him. That's his way of playing the ukulele just like the ukulele master Ohta - San using only thumb with long nail. Kimo's way of playing the ukulele is to play the bass string (Kimo used Low G) with the thumb and pick the melody with his index. He combined the two together and create his own style of playing the melody and harmony SIMULTANEOUSLY.
Is it really only Kimo Hussey? I feel like I've seen it elsewhere, though it's not how I play, and I don't know much about this playing style. I do recall once seeing a group where fingerpicking novices were encouraged to use just their thumb, index, and middle in the style @ripock described. After that, I assumed there was no single formal method to fingerpicking on the ukulele.