In that case you can’t use LWJGL either. You’ll have to write your own OpenGL library from scratch. 
Really, there’s nothing wrong with using these libraries, they don’t make you a “lesser programmer”. This isn’t like graphics or web design where using a template/google images is frowned upon and makes you look like an amateur. I mean hell, look at all the Triple-A titles built up on someone else’s 3D engine? It’s commonplace to use other people’s boilerplate work and build on top of it in the programming world. No one will think any less of you.
In my project, I use Slick2D and Trove. No one thinks less of my project because of it. It saved me countless, and countless hours of boilerplate junk code that would of not had any real impact on the final product’s quality. …and like Cas said, based on the screenshots you provided, you’re way over thinking this. You could probably do what you’re wanting to do in Java2D/FX if you wanted to. Although I would recommend using LWJGL/LibGDX though. Be silly not to.
Now, if you just want to learn lower level OpenGL code, sure, toss LibGDX aside. But really, unless you want to learn for the sake of learning; don’t bother.
Final after-post though: Think of LWJGL, LibGDX, Slick2D, Trove and all the other libraries as “tools”. Not “shortcuts”. 