I think your understanding is backwards. The particle is highlighting the word that comes before it. So in your example sentence above, it’s not that meat being emphasized, but kore.
My understanding for these types of sentences (where it feels like both が/は would work), is that が will be able to specifically respond to the question being asked.
For example, let’s say a set of meals has just arrived and one of them is vegetarian. Someone might ask who it is that doesn’t eat meat. In that case, you could respond using the が particle because you’re emphasizing that it is you that doesn’t eat meat out of the group of people (私が = I am the one… (that doesn’t eat meat)).
I am also a beginner, but this is how I’ve been able to make sense of the particles. I hope this helps you a bit.