The first time this poem appeared was in 1830, so it is a relative newcomer as far as traditional English rhymes go! However its popularity was such that it has appeared in nursery rhyme collections ever since.
I Love Little Pussy is simply a way of telling a child to treat the pet gently.
I Love Little Pussy Lyrics
I love little pussy, her coat is so warm,
And If I don’t hurt her she’ll do me no harm.
So I’ll not pull her tail, nor drive her away,
But pussy and I very gently will play.