I know all about that move. That was my semi-nemesis move when I first started, and has turned into one of my go-to moves that I LOVE. I had to learn the mechanics of it before I could actually do it.
So, this spin: Hooking your inside leg is your anchor, it keeps you at the right distance from the pole, and provides some support (though, on static, I would advice against gripping too hard, because that hurts if you're wearing shorts!). Your arms are also going to be providing support by way of lift... but it's usually the position of the hips and spine that get people.
The hips have to be FORWARD. I know how freaky that is. But, if you create a straight line all the way from your shoulder, down your side, through your hip, to your knee... you'll have better grip with your leg. You will no longer feel like you are going to fall off. Crunching up and leaving your hips behind the pole will make that feeling far stronger.
As Dustbunny said, around here we tend to teach spins a little later, because you can really wrench your joints (particularly shoulders) when doing them. I learned this spin a mere four weeks into starting pole... probably not a good idea, considering I was fairly unfit and was not working on any kind of strength! So, please be careful. Remember to engage your lats, protect your shoulders with them. It'll save you a world of issue later.
This spin does have it's variations, like keeping your legs together once you've pushed off, and also doing it one-handed, but I prefer the legs-open version.
Fireman spin is awesome, and you'll use it for the entirety of pole dancing! I also find that I use a lot of my "beginner" moves all the time, just... sort of to cool off from bigger tricks, or even as a warm up before I actually start working on said tricks. Pirouettes, half spins, slides, floorwork, footwork (such as the cross-step that Veena has on here), holds, and all of that stuff is stuff you'll use forever. It is what makes it a dance, rather than a series of tricks!
You'll get this one. This spin is almost like a leap of faith... but eventually, it becomes a kind of falling into awesomeness. If that makes sense ;)