Very few people really are in a position to be unable to learn to snowboard and that is usually do to either being seriously out of shape or a physical disability. Many of us did go through frustration in our first few days of learning to ride so that is quite normal. I never really considered giving up on but I will say that there was more than one occasion where I became so angry that I threw my board into the woods only to have to wade through snow to get it when I cooled off.....
I think the best course of action right now is to provide an outline of what your instructor covered and what he/she told you to do. Not every instructor is equal and additionally, group dynamics can be a major impediment to progression and that may not be the instructor`s fault. I have had groups that I flat just could not seem to connect with and as the coach, I walked away from the end of the session more frustrated than the clients; it happens.
I will be happy to work with you as I have with Vicki (firstx1017) over the course of a couple of years on this forum to help get you past this. Before proceeding, it is best to get a grasp of what you are doing and how you are doing it. I am not in agreement with a few here who are telling you to go to steeper terrain. While this method does work for some, it will not work for everyone and generally the last thing you ever want to do in snowboard progression is introduce new or more complex tasks and more challenging terrain at the same time. Stick to the terrain you feel comfortable on because you need to feel safe before you will be receptive to learning.
I would encourage you to watch my video of a typical first time lesson. The only real change from when I did this (other than I like to think I am a better rider and better teacher after 8 years of doing it) is the Falling Leaf. AASI no longer advocates this and I now totally agree with AASI on this.
Beginner Snowboard Lesson Part One
Skating, gliding and stopping
Beginner Snowboard Lesson Part Two
Loading / unloading the chairlift and getting up after strapping in
Beginner Snowboard Lesson Part Three
Sideslipping and Linked Traverses heel and toe side
Beginner Snowboard Lesson Part Four
Garlands and basic turns
Take a watch of this and then get back to us with a review of what you experienced in your lessons.....