[coldtea]

>Your parent just explained, that there have been animals hatching from eggs before there were chicken

And I just explained that that alone is neither here, nor there, as the paradox is about the chicken egg, specifically, not whether eggs existed in general.

>At some point some of those egg-hatching animals had mutated enough to be now called the first chicken

Yes, but that's a different answer, which wasn't available when the chicken/egg question was posited - and it still points to a random (evolutionary) and fuzzy (when? how?) process.