There are more kinds of houses in this story than appear on one day of HGTV programming. (Don't know what HGTV is? Then you must not be a yuppie.)
In stanza 2 ("You have brains in your head./ You have feet in your shoes") we see a Seussian version of the suburbs: neat, well-maintained houses and yards, each safe and sound in their straight little rows. Here, houses are clearly a symbol of childhood. And boy oh boy, is your kid racing away from that!
But by the time we come to stanza 15,
You will come to place where the streets are not marked.
Some windows are lighted.
But mostly they are darked. (15)
Houses have taken on a totally different meaning and look. Now they're completely foreign, full of confusing spirals and curled domes, painted weird colors, and, in some cases, completely dark and uninviting. Your child may have found houses, but they're pretty far away from home.
By stanza 24,
Except when they don't.
Because, something, they won't. (24)
We see the wacky, fun, whimsical home your child's adventures have brought them… and what it looks like when they lose it all. Now home is once again something that must be walked away from in lieu of the wide-open, intimidating road.
It's not exactly clear whether the home your child will ultimately find will be a giant mansion or if home is wherever I'm with you, but one thing is clear: your child isn't just searching for a way to move mountains; they're searching for a home that's every bit them.