Of course it's way too early to give up on skating. Hope you keep on going, and have fun doing it!
Not lacing the skates firmly enough or all the way up, skates too big, skates broken down...
Yes. As a former skate guard, I'd say these are the most common problems. Literally the majority of relatively new skaters get skates that are too big (they should be somewhat smaller (in the U.S. roughly 1 size smaller, though that won't always apply, and it also varies a lot by brand and the shape of your feet) than regular shoes) and don't lace them tightly enough, or not all the way. Skates have to be a lot more snug than normal shoes. For a while, I tried to help them check whether they did it right, but most people don't want to be told they have tied their boots wrong, or that they don't know their boot size.
If you see someone who looks like a good skater, you could ask them if you have laced tight enough, if the boots are too big, or are too broken down.
Also, you probably shouldn't be too afraid of falling. Hopefully they taught you how to do it without hurting yourself in the first lessons.
It's also a good idea to get some practice outside class. If you figure out the balance thing, it will be easier to enjoy class.
If you can afford it, you could approach the teacher and ask whether you could have a private lesson to help you figure this out. If there is no problem with the boots, that is one of the best ways to solve problems, though I admit it can be expensive. It's very difficult to give much private attention to students inside a group lesson.
This is a bit technical, but to have good balance, it helps a lot if the entire bottom of your foot is in contact with the footbed of the boot, with roughly equal pressure on both sides of your foot. E.g., if only one side of your foot is in contact, or has much stronger contact than the other side, you may tend to fall towards the other side. That's not something easy to fix in rental skates. I helped some people by suggesting they fold up some toilet paper from the rest room, and put it under the foot with no contact. That's a very temporary solution, and not a very good one, but a rental place wouldn't want you to modify the boots.
In terms of gliding forwards, it helps a bit if your heels are a bit closer together than your toes on the ice, when both feet are on the ice..