I have found over the years that rhyming is a lot harder for children to understand than you would expect. I can give you a few theories I have, but remember they are just my thoughts!
First, often times children listen to the first sound of a word and then make assumptions of the word based on context or background knowledge. This is very evident when children begin reading. They will look at the first letter and then just guess a word with that beginning sound.
Also, children are typically better at picking out two words that rhyme than coming up with words on their own. Again… children see/hear words based on the first sound and with rhymes you need to hear the rime of the word not the onset. They also have to have the word sense and vocabulary to pull words out of their memory.
There are lots of ways to play with rhymes and they are all important! When working with rhyme, I usually start with poems, song and stories that have many rhymes. Songs and poems can be memorized and then adapted. This is why children enjoy nursery rhymes and songs such as Down by the Bay by Raffi.
There are many online rhyming games, such as these games on PBS Kids. But you can also make your own rhyming games at home.
Play I spy with rhymes. I spy something that rhymes with head– bed, red. something that rhymes with hair– chair, pear. etc…
Sing head shoulders knees and toes, but put in words that rhyme with the body parts instead
red, boulders, trees and rose
bed, folders, please and grows
skies and years and south and does
bread, holders, sneeze and hose
keys and snows
Make it fun! Play games with rhymes all the time. They will get it… it will click. Have fun