The Itsy Bitsy Spider was first published in 1910 in a camp lore book as an adult song. Except it was originally the "Blooming Bloody Spider." I'd much rather have a tiny spider than a bloody and expanding arachnoid, so I will keep using "Itsy Bitsy." I found all this out from Wikipedia if you're interested.
As one of our good friends (DT) pointed out, Itsy Bitsy Spider is a song about hope, which is why Evie likes it so much. I did a quick analysis of the note in my head and it's just 5 notes over and over again with a surprising dip at the last phrase. C, D, E, F, G and a low G. Twinkle Twinkle Little Star had more going for it with more notes. Row Row Row Your Boat has similar usage of notes, and yet Evie sticks up her nose at it. My best guess is that she likes the simple melody and the rhythm and doesn't care at all about the spider.
This brings me to nursery rhymes. Did you know that Mary really did have a little lamb who went to school with her one day because her brother told her to? The moral of the story is to listen to your brother because you may become the stuff of legends. Baa Baa Black Sheep has its origins tied to a medieval wool tax. I didn't realize it was so serious when I was singing that! Anyway, it doesn't really matter what we are singing, because it's the music and rhyming that are helping with Evie's development. That's a good thing, because half the time I have no idea what the words are!