When studying sonnets or other poems, why do we analyze the stressed and unstressed syllables?

The author had a rhythm in mind when he/she wrote the piece. If you don’t get that down how are you living up to what the author had in mind? Is that simple enough for a teenager?

Meter and stress are the underpinnings of traditional English poetry (as well as poetry of many other languages.)

English is, by its very nature, a stressed language.

The oral tradition uses the beat in order to make memorization easier.

Buy her the classic book by Paul Fussell, Poetic Meter and Poetic Form

This is my bible and takes several hundred pages to answer your question.

Poetry is not simply sentences strung together with end rhymes. The meter and form are an innate part of each poem.

Shakespeare’s sonnet form is a very rigorous one. That is not an accident. Has anyone analyzed for your daugher why a sonnet is a sonnet and not a villanelle, for example? Google will give you some straightforward explanations.

Remind your daughter of the forms of music and the forms of painting and sculpture. Brush strokes themselves matter along with the five shadows, the art of perspective, the use of light and dark, and color..A sonata or symphony has a form.

The meter is often just as important as the rhyme.
Words in English have syllables that are and are not stressed. By arranging these syllables into a pattern, we create meter, just as we create rhyme by arranging syllables with the same sound.

As @gailcalled said, better than I ever could or would, it’s the form that makes the art. Free verse, such as that written so well by e.e. cummings and others, is its own art form, but the structure, meter and rhymes of Shakespearean sonnets are a form unto themselves.

Maybe you could simply point her to Fluther and some examples of her writing here and suggest that if she works, pays attention and cares enough, she might someday be considered as bright and as cultured in her adulthood – or even relatively soon, if she works hard enough – as @gailcalled herself. Or Milo.

Not that you have time for this, but teach her a few drum rhythms. Then ask her to memorize words with a strong meter and those without. Then ask her to memorize words with melody as compared to those without.

These forms have to do with oral tradition somewhat, and tricks to make things easier to memorize, and also to do with structure that forces the poet to be very creative in order to make things fit in the pattern he is using.

Structure sets you free. It is all part of the process of creativity, and it makes amazing things happen. As Shakespeare proved, over and over.

But these things are all difficult to understand until you do them yourself.

In a sonnet words are not just chosen for their meaning but for their sound and their rhythm when spoken together. The words become a chant and flow like music into our minds and become a unity, a poem, which is greater than the sum of the individual words. We analyse stressed and unstressed syllables to try to understand why the sonnet works and how best to recite it. It is a means to an end and pretty dry and uninteresting of itself.