Learn Turkish: Et bozuluyor, bunun için kedi onu yemiyor. - The meat is going bad, therefore the cat is not eating it.

It literally means "for this" (bu means "this", -nun makes it "of this", and için means "for"). In Turkish, saying "for this" is a very common way to say "therefore" or "that's why" to connect a cause to its consequence.

Is the verb "bozuluyor" related to the word "bozuk" (broken)?

Yes! The root verb bozmak means "to break" or "to ruin". The suffix -ul makes it passive, so bozulmak means "to get ruined". When talking about food, it is the standard way to say it is "spoiling" or "going bad".

The verb is "yemek" (to eat) and the negative is "-me". Why is it spelled "yemiyor" and not "yemeyor"?

This is due to a rule called vowel narrowing. When a verb or negative suffix ends in a wide vowel like a or e, adding the present continuous suffix -iyor squeezes it into a narrow vowel like ı or i. So, ye-me-iyor becomes yemiyor.

Why do we use "onu" here? Can't we just say "kedi yemiyor"?

If you just said kedi yemiyor, it would mean "the cat isn't eating (at all)." Because the cat is refusing a specific thing we already mentioned (the meat), Turkish requires you to include the direct object onu (it). The -u on the end is the accusative case ending.