Ah, I once felt like this . . . but it was when my children insisted on bringing bugs into the house and letting them reproduce! LOL It can help to tell yourself you are changing your mind . . . "I DO like praying mantises . . . I DO!" LOL
I love poetry and have my entire life, except for a few years in high school and college when I was briefly frustrated by teachers insisting I massacre the poems to bits instead of enjoy them. So I am very, very biased. :-) You'll live, and we'll all still let you hang out with us if you never love poetry. It's hardly the make-or-break issue of life. :-) However, your children enjoy it, and it'd be easier on you if you at least could manage to call a truce!
One thing I think can be helpful is having someone around to discuss poems with. I have a good friend who is, um, less enamored of poetry than I am. Specifically she once really didn't like Emily Dickinson, who is probably my favorite. We were on a list that discussed what we moms were reading, and I got to share some poems and why I liked them. I don't know if Dickinson is yet my friend's passion, but I do think she ended up liking her better than she had before anyway. Sometimes having someone to discuss a poem with can be a big help.
So can just simply asking yourself and your dc some simple questions. Why did the author say that, use that image, use that word, flip those words into a weird order? Can one really see the world in a grain of sand? Is this possible? Does it make sense? Can you think of a better image? What image would YOU use if you could?
A whole book might be a bit much for you to start with, but I want to recommend a beloved book of mine, by a Christian author, who does indeed make a case for why poetry matters. It is The Roar on the Other Side, by Suzanne Clark. It is actually for students, and there are exercises in poetry writing, and sections on things like meter, but you wouldn't need all that stuff right away. For starters, the discussions on seeing like a poet should be a help to you I think.
Here are a few quotes from the book as something to think about:
"In every poem there is some of the substance of God." St. Augustine. OK, I might have to differ with this a bit. I think this is true of MOST poems. St. Augustine fortunately never read Allan Ginsburg (NOT a recommended poet, IMO!) But think of this when you read. What facet of God is reflected in the poem in front of you?
"God made our minds to love him . . . We love God with our mind when we admire smoothness, strangeness, motion, structure, intricacy, fragrance, complexion." "So, then, noticing what God has made is important. In noticing, we name. Thus Adam became the first poet. He named every striped, spotted, winged, webbed, slow, swift creature. He was creative."
There are some real delights in this book. I think it might be a help to you, and I'm almost certain your children would like it, if they are too young now, then at some point. Might be worth tracking down!
And anytime you want to IM me about a poem I'd be delighted to enthuse about it long enough for you to catch a little. :-)