What does this rhyme symbolize? What does the ladybird symbolize? Ladybird, ladybird fly away home,Your house is on fire and your children are gone,All except one,And her name is Ann,And she hid under the baking pan

This rhyme, sometimes attributed to Mother Goose, is a nursery rhyme: a folk verse typically taught to young children and handed down orally for generations. Some nursery rhymes have historic meanings that most modern readers don't understand. For example, several explanations of "Humpty Dumpty" give it meanings from British history, and "Ring Around the Rosie" may have originally referred to the bubonic plague.
Some have suggested that "Ladybird, Ladybird, Fly Away Home" may refer symbolically to the persecution of the Catholic Church in England after Henry VIII withdrew from the authority of Rome. In such an interpretation, the "Ladybird" (the British name for the insect that Americans call a ladybug) represents the Virgin Mary. Telling the ladybird to fly away home suggests that followers of the Catholic faith should leave England and return to Italy, the home of Catholicism. The references to fire and the loss of children could refer to persecution of Catholics via the burning of churches and killing followers of the religion.
One need not concur with that interpretation to find symbolic meaning in the rhyme, however. The best way to determine symbolism is to look for parallels between the symbol and some real-life person or quality. A ladybug is an almost universally appreciated insect, contrasting starkly with other creatures in its class. Most people will slap a mosquito, swat a fly, or squash a spider underfoot with not a second's regret. Yet most people will shoo away a ladybug instead of killing it. This rhyme describes such a merciful action toward the tiny critter. The little bug is told to fly off and given reasons to hurry away. Although the warnings are dire, this may be interpreted as a harmless way to encourage the ladybug on its way. The description of "Little Ann" is further proof that this insect is endearing rather than loathsome; our hearts immediately go out to the sole remaining offspring who is hiding under the baking pan. Ann gives us all the more reason not to harm the ladybird; we don't want Ann to be an orphan in addition to having lost all her siblings.
Thus, one symbolic meaning of the rhyme is that Ladybird is any representative of a normally despised or ill-treated class who is shown mercy rather than cruelty. Ladybird could stand for a wild youngster who, when caught in a youthful indiscretion, is left unpunished by the authorities. Or, Ladybird could be a woman who is excused from an odious task in order to protect her sensitive nature.
Alternatively, perhaps the rhyme symbolizes wanting to get rid of a "pest" who is bothering you. However, such an explanation doesn't seem to fit with the emotional picture of "Little Ann" hiding under the baking pan.
The rhyme presents several possibilities for symbolism. It could be used to represent many situations, depending on the context in which it is used.
https://www.poetryfoundation.org/poets/mother-goose