We are not born with an automatic ability to understand and speak our mother tongue, but we all learn it through consistent exposure and consistent practice. Likewise, we are not born with a natural ability to understand and produce music, but it is learned in the same way as language: through consistent exposure and consistent practice.
Exposure is key. In the case of a child born deaf, they will never speak their language clearly, despite all the practice in the world, because spoken language is first acquired through the ears and only then produced accurately with the mouth. Music is like language in this way; all the practice in the world cannot make a good musician if they do not intentionally lay a foundation of listening.
Nobody should despair their musical inability any more than they despair their inability to speak some foreign language, because they are both skills that anyone can acquire, given the right guidance.
The process employed on this site is known as "ear training", which is the process of developing aural (as in "listening") skills and musical intuition through the use of structured exercises. As the title "Aural Foundations" suggests, these exercises are not "chanting" as such, but are a good way to train specific skills, such as singing in tune with a drone, which are essential and foundational skills for everyone who wants to chant.
Most ear training programs online use western theory, including chords (major, minor, etc.) and western interval names, which are largely irrelevant for students of Byzantine chant. Here the exercises focus on skills relevant to vocalists, and use the Byzantine parallagi:
Νη Πα Βου Γα Δι Κε Ζω Νη
Ni Pa Vou Ga Dhi Ke Zo Ni
Importantly, a complete ear training program for Byzantine chanters must include lots of listening to recordings of skilled traditional chanters. Byzantine chant is an oral (as in "spoken") tradition, passed down through the life of the Orthodox church, and there is much that can only be learned by absorbing authentic chanting. The exercises on this site will never fill this role. Here are some good traditional chanters you can listen to:
Panagiotis Neochoritis (Παναγιώτης Νεοχωρίτης)
Dimosthenis Paikopoulos (Δημοσθένης Παϊκόπουλος)
Ioannis Liakos (Ιωάννης Λιάκος)
Go to Exercises and train your ear.