I think we should be honest to ourselves. Humans are different and don't all have the same motor skills. Some have very good motor functions, others have not. And I think those with very good motor functions learn to play the violin easier, especially if it comes to vibrating. Another question is how good one is in multi-tasking if it comes to motor skills. Some easily learn to make their hands do different things at one time until their left hand seems perfectly independent from the right hand. Others struggle a lot with it. I think this is the problem, if you have to hold the violin still and vibrate with the other hand. I know I'm not good at this and that I'm a slow learner. I have developed my own very thorough and effective strategy to compensate it, but this will not help me in things vibrato. That's why I procrastinate it—maybe I will wait years before I'm ready to work on vibrato. I must be technically absolutely safe and relaxed before I dare it, otherwise it will make things worse. In baroque I hardly need vibrato anyhow.

Fiddlerman said
No-one can vibrate perfectly forward and back. There will always be a slight amount of right and left going on.
The pain in your arm is coming from tension.
Relaxation while playing is an art in itself. As a player new to vibrato you may be using more tension than necessary, even if your arm seems relaxed.  

I know I would have more  tension! That's why I stay away from vibrato until me playing the violin will be almost as easy as walking on clouds.

Having started this morning with an improvisation over an adagio out of a Bach sonata, which is 8:42 long these thoughts: This is the longest Edition Peters play-along I know and I can only play almost 9 minutes because it's a very slow adagio. At 2:00 I feel very fresh, my violin is warmed up and sounds great and I'm relaxed, just enjoying my own music. At 8:00 I try to keep being relaxed, but it's a little difficult, because my wrist feels tired. That's the reason why I'm now pausing. If I had continued with the next track/movement, my hand, my harm, my shoulder would now hurt. Pain makes the body automatically tense. I need discipline to stop playing, because something inside my head wants to play on, but I know, a relaxed technique is only possible if I pause now and then.

These days I'm successful with an exercise I 'invented' (it probably isn't new) in May, but I wasn't on a level to consequently practice it: It works like drumming with fingers on the table. With four fingers it's possible to drum nice rolls on the table and I can do it on the fingerboard as well. It works best in G major pieces and I can do it up and down. Down sounds like "deedle-up" and I can connect it with an up like "deedle-up-doodle-ip". I think this is a fairly relaxed thing and it helps to relax my technique a bit more. But it's also very dangerous, because too much of that medicine is poisonous again! Because if I practice this again and again, my wrist tires very soon and then it's painful.

We must watch what we're doing and constantly 'listen' into our hands and arms, to hear the warning signs. Are my hands and arms still happy or is it already beginning to be torture? Then pause.

I'm very sure, practicing vibrato to long is torturing my arms. You feel it in the wrist very soon and then it's time to stop and then probably do something else. Wanting vibrato too badly, especially if it's to early, is very poisonous to the technique. I've tested that too and I found it bad, bad, bad. It it felt like the safest way to tension. Beginners should learn to be happy with playing the violin without vibrato and wait, wait, wait. But somehow the idea these days it, that people find violin vibrato very touching, feely and downright sexy. It has to do with ideas about love and happiness and has become sort of mass hysteria. It seems, many young people feel like, if they can beautifully vibrate on a violin, they will be loved by the rest of the world. It seems to be and expression of human yearning for love in our western culture. Which is resulting in beginners wanting it too badly and too early, which makes it very harmful. Just clear your head and try to be reasonable. Play for yourself and not for other people to make them love you.

I can use vibrato in ancient music now and then and someday I will. I also like mushy 30s music and there you need it a lot (I have been an old-style crooner since the 80s). But I certainly wait--possibly years. For learning to play a musical instrument we need lots of discipline and patience.

I think vibrato should be a natural thing, which grows naturally. It comes from singing since vocalists inspired instrumentalists to imitate it. We are thinking too much in our western culture. I concentrate my thinking on really scientific things in music, like harmonies. I watch carefully whether the tuning is right and my fingers hit the right places on the fingerboard. I also watch my body kinda like a physician, to avoid tension, control the duration of playing and then give myself order to pause. In these things I'm extremely intellectual. But I refuse to ponder all things which have to do with expression in technical ways. In the beginning there is a point where I think how but then I just let it go.

Learning an instrument takes at least about five or six years. Until then you cannot be perfect. Vibrato is also something that grows over years. Investing into a huge pile of CDs of good players is always a useful investment. The intellect is not much help in this matter. It goes into your heart when you listen and spontaneously comes out of your heart while playing. You have to listen to a lot of vibrato in order to under stand it by heart. Nonetheless the speed of vibrato will grow slowly and can't be forced. We are no robots which can be programmed just like that, human learn slowly.

Wanting too much and too hard leads to tension. The intellect abusing the body—the kind of violence people do to themselves.

Natural music is never mechanistic. That's why music created via midi-synthesizer doesn't sound natural—because it is too even in a mechanistic way. The personal sound of a human will always be a little uneven and that's natural and beautiful.

I fooled around with midi a lot in the 90s, considering it a great chance to create any kind of music. Finally I came to the result it's dull and dead. Interesting to compare my keyboard harpsichords before last summer to what I play on my spinet now. The keyboard is dead, its sound is too perfect and simply not beautiful.

Perfection can be a dangerous trap. In the New Orleans Jazz community (I was part of in my young days) I met many who consider musicians dull who technically are too perfect. And I agree: there are examples of musicians who lost warmth over the years, while gaining technical perfection. Amateur bands can more warmth than that.

Thinking about teachers of classical music again: some of them aim at a level of perfection I can not approve. I might go on with a teacher some day, but will carefully choose. That person must be more open-minded than the average.

Interesting the discussion about pianists who play with flat fingers. That's a bad mistake in classical piano teaching. In jazz there are examples of great virtuosi who do exactly that. As long as they are beginners, people will criticize them, later they will praise them like saints. Then it's called "alternative technique"! See there, that's what I'm aiming at right now.... Let them talk!

I've tried vibrato a week or two ago and now don't consider it a problem. But I have no time to work on it, since I'm working on more basic and important things in my personal violin style. But some day I will just start doing it now and then. I will start it in very slow pieces and  then slowly raise the tempo level. And I will not practice it, I'll let it come.