Would you ask a little girl in gymnastics class to do this without jumping off?
Would you ask an Olympian to do this without swinging?
No? Then why would you ask your pole students to do as much?
Momentum in pole pedagogy is ironically taboo. "Ironically" because the spins and swings which are at the origin of Western pole dance are almost entirely momentum-based. And yet some teachers forbid their students from jumping, kicking, or swinging into various moves. "Muscling" any kind of inversion is seen as the "right" way to do it, and using any kind of momentum is "cheating," and even decried as unsafe.
Also ironic because most teachers themselves learned the very same moves by using momentum. But now that they've gotten it into their bodies and gotten so used to it and had so much time to train it that they can muscle it, they realize that they were "wrong" and are going to keep you from making the same "mistake."
It's funny, because it's only in pole that I really see this. Way back when in circus school, we were encouraged to use momentum in certain kinds of inversions. I once trained silks with a high-level professional aerialist who asked me why I kept muscling my inversions. And much of gymnastics would be impossible without a running or a swinging start.
Momentum isn't what you should be afraid of. You should be afraid of flailing. In my studio, it's OK if a beginner jumps into their inversion--heck, I don't deadlift most of the time I'm working from the ground, especially if I'm in a tight space--but it's not OK to spastically throw your outside leg to the pole and hope you hit close enough to kick yourself over.
Momentum is about flow. You go with the energy, like you're riding the wind. You should never jolt, even if you're throwing something hard. I often use the term "hard throw" when talking about certain spins, but it's about the amount of energy in my movement and the angle of my extensions, not any kind of force. A pitcher who throws a ball hard can do it with ease and flow, or by forcing it. When they force, they dislocate a shoulder or tear a rotator cuff. Same thing with you.
They can also hurt themselves by overdoing it over time, and so can you (and so have I). Practice your moves on both sides, and don't overtrain the same moves over and over, especially when they are new to you. (See Reasons to learn tricks on BOTH sides and Are you overtraining?)
Reading over testimonials my students have written about me, I am known as being a trainer who promotes strength. But professionals know that muscling everything is an inefficient use of energy. It's great to build up the strength, but if you've got a dozen shows a week, you can't be wasteful.
Nonetheless, it's good to be able to work up the strength to deadlift as many moves as possible, for the sake of control as much as for showing off. After all, if you're going to get yourself in a tricky position, you need the muscle control to be able to get out of trouble if something goes wrong once you get there.
Meanwhile, how do you use momentum without flailing? A lot of it is psychological, not letting yourself tense up or hold back. Remind yourself to ride the wind instead of thrashing about. Easier said than done when working on a new move. More technically, it's about paying attention to your form. You can't just think about getting to the end position by any means possible. You have to know the position of your body, even if you're upside-down and the world is spinning around you. Here I tuck, here I twist, here I extend. A good teacher should be able to tell you the sequence of movements and as many subtleties as possible. But ultimately, you're going to have to find the sweet spots yourself. Until you get there, pay very close attention to your coach's instructions. It's more important to think "hips up" than to think "nowwww GO UPSIDE-DOWN!!!" If you keep good form but you don't make it all the way, that's OK! Better to learn good habits in the beginning.
There is a time to muscle and a time to ride the wave. Having good technique in both cases is the end goal.