Either, or eye-ther

Is it eether or eyether? Both. The pronunciation is yours. The rhyme follows.

English is full of these forks. Caramel has two syllables in some mouths and three in others. Pecan shapeshifts depending on whose grandmother taught you the word. Either can land on EE or AY and both are correct.

This used to be a problem for rhyme. The dictionary picks one. The neural network picks one. But you, the writer, might want the other.

Variants

The fix is simple: let the word have more than one face. Pick the one that fits your line. If you want eyether to rhyme with fire, you can. If you want it to rhyme with breather, you can do that too. Different song. Same word.

Your ear is the authority. The dictionary is just a suggestion someone wrote down.

The point of writing is precision. Precision means picking the version of the word that says what you mean — in your voice, in your accent, in the song you’re actually singing. There is no neutral pronunciation. There’s only yours.