Ray, do you have any authoritative opinion that they don't? I only need my ears to decide when two words rhyme.
What a strange question. Of course I have authoritative definitions of rhyme that show that 'oot' and yoot' rhyme.
"A full rhyme is the identity of the last stressed vowel and all the following sounds of two or more words or phrases"
Dictionary of Literary Terms and Literary Theory. Cuddon, Penguin.
The vowel is not the only thing that determines a rhyme. 'Cute' and 'cube' don't rhyme because a rhyme does not depend just on the vowel. I can find other similar definitions, but I think the definition of a proper rhyme is too well-known to bother looking them up. But there are different degrees of rhyme. If ears are all that's necessary, I can say that 'cute' and shoot' rhyme too, because I also have ears. But what is also needed for a correct answer is a definition of rhyme.
Now that I've answered your request for authority, why don't you answer mine?
Besides, I don't think this is answering the OP's question. He's probably given up in disgust by now, or gone to another site where they've tried to tackle his question. If he's actually asking whether 'cute' is pronounced 'kyoot' or 'koot', which is possible, then ems and I have answered him. They're not.