Why it is called chicken egg problem and not egg chicken problem?

Because if egg was listed first, people might start thinking of eggs that didn’t come from chickens, and the riddle wouldn’t work.

Prose.
Chicken and egg sounds better than egg and chicken.
Or even just alphabetically, chicken comes first. Which I guess would also answer the question of which came first... 🤔
- In Germany we say Hühner Ei Problem (chicken egg problem). So i don't think the alphabet is that important.

Technically it is not a problem, a mutation happened and the egg was now going to create a different version of the parent. Whether you checked the DNA of the egg or when it was older it would be the same species, but different from the parent, and the parent did not change.
- It's a problem of definitions.
  Is a chicken egg an egg layed by a chicken, or an egg from witch a chicken will hatch?
  
  :) A chicken is a discernable species, this species differemtiation happens at the egg; regardless if the egg was laid by a dinosaur.

I think for some reason it flows better when you call it chicken and the egg.
However there's some weird phenomenon like saying "tick tock" flows better as opposed to "tock tick" and I think that's called ablaut reduplication. Don't think that's with the egg and the chicken though.
Btw for the root question, here's a QI bit on it: https://www.tiktok.com/@theqielves/video/7415894774202240288

I'm not exactly sure what you mean, but..
Which came first, the chicken or the egg?
Neither can cum, the rooster came first, obviously.
The more you know...