A paradox is something that can’t rationally be explained (by mortals).
You can debate whether the thing you don’t understand includes xyz or not, but you can’t really be authoritative on it (without immortal sources).
What exactly are you trying to be authoritative about? I don’t really get what you or HaLeiVi are trying to address.
Also, your definition of the term paradox is not accurate (or at least irrelevant as it applies to this particular case).
Additionally, in what way can infinite be relative? Please give an example.
In its different applications. You are right the the absolute concept is absolute, but so is the absolute concept of bigness. Relativity can only exist in specific applications, of which there are plenty relating to infinity – that is what set theory is pretty much all about. One example – the cardinality of the set of integers (…-2, -1, 0, 1…) is infinite. However, the cardinality of the counting numbers (1, 2, 3…) is also infinite, although the set of counting numbers ostensibly contains fewer elements. (Yes, this is a paradox, but I don’t see how this makes a difference to any of the arguments that are being made here.)