I would suggest that the theme of the poem is one which speaks to the age (or generation) gap which exists between the youth and Father William (his father). It is surely a satire and meant to be found humorous.
Carroll does an excellent job of, No pun intended, standing poetry on its head! He uses what would have been a conventional style (modelled after the poem above) but the words are the opposite of what we expect. If read as it is, the youth seems to be the practical one, while Father William is somewhat ridiculous. The comedy (and the irony) is that we know that Carroll, and any adult reading it can see that the opposite is true. Certainly the poem is also used to created the sense of upside-down world that Alice is experiencing. First, she says that the words "aren't quite right". What is happening in Wonderland that her recitations come out strangely? And second, what is wrong in Wonderland that youths are so serious and elders so silly?
Much of the humor of this poem derives from the fact that it is a parody of a more serious, conventional, and predictable poem by the poet Robert Southey titled "The Old Man's Comforts and How He Gained Them" (see below). Carroll is having fun with Southey's poem by turning it on its head (no pun intended):"You are old, father William," the young man cried,"The few locks which are left you are grey;You are hale, father William, a hearty old man;Now tell me the reason, I pray."
"In the days of my youth," father William replied,"I remember'd that youth would fly fast,And abus'd not my health and my vigour at first,That I never might need them at last."
"You are old, father William," the young man cried,"And pleasures with youth pass away.And yet you lament not the days that are gone;Now tell me the reason, I pray."
"In the days of my youth," father William replied,"I rememberd that youth could not last;I thought of the future, whatever I did,That I never might grieve for the past."
"You are old, father William," the young man cried,"And life must be hast'ning away;You are cheerful and love to converse upon death;Now tell me the reason, I pray."
"I am cheerful, young man," father William replied,"Let the cause thy attention engage;In the days of my youth I remember'd my God!And He hath not forgotten my age."
The theme comes from humor, and satire. Carroll is known for funny poems with meaningful messages. I'd say one theme of this one is that children rarely really understand the adults in their lives, and what they have been through.
thank you!!!!!! :)