Humility is in Andersen's writings almost always connected with persons' being world-oriented, thus often also against its creator, God, or being self-centered. Self-satisfied and self-sufficient characters are often exposed in Andersen' oeuvre. Their charateristics are pettiness, intolerance, a narrow mind, insensibility, being ungratified, because the world seems cruel and unjust and doesn't give them enough, and arrogant pride. The proud and self-sufficient persons thinks that all that is good comes from him-/herself. The humble sees the world around her and her own conditions as sent from God. The humble is satisfied with the facts of life and even thanks (God) for everything.
The rose in "The Snail and the Rosebush" is, in contradiction to the snail, a pious grateful and extrovert type, giving its best to the world. "The Snail and the Rosebush" is a textbook example of the motif and is in addition extraordinary, because God isn't mentioned explicitly as the source of the gifts of life.
They [the poets] and I have been given a divine gift, a blessing great enough to satisfy oneself, but altogether too little to be portioned out again to others. It comes like a ray of sunlight and fills one's soul and thoughts; it comes like the fragrance of a flower, like a melody that one knows and yet cannot remember from where.