Your parent just explained, that there have been animals hatching from eggs before there were chicken. At some point some of those egg-hatching animals had mutated enough to be now called the first chicken. He thereby answered the chickend-egg-question through evolution.
Edit: Even if you specify, that it has to be a "chicken-egg" you just have to decide, whether an animal producing a chicken-egg is automatically a chicken. I would argue no, because you could then prove by induction that everything before has been a chicken.
>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.
Edit: Even if you specify, that it has to be a "chicken-egg" you just have to decide, whether an animal producing a chicken-egg is automatically a chicken. I would argue no, because you could then prove by induction that everything before has been a chicken.