Overthought theory
"A man without a penis is no longer seen as a man"
I think this is Jax's problem
Jax, as a man, entered the digital circus, and as a consequence of being in the circus, he had a hollow avatar with nothing, "no genitals," and the penis, in many cases, is the man's identity. By losing that part, Jax somewhat lost his human identity and masculinity, and perhaps that's why he began to believe he was a caricature.