Here's why:
* "Master of its own house" is a metaphorical expression. It doesn't literally mean that a hemisphere has a house or is in charge of a physical dwelling.
* The metaphor is used to convey the idea that the hemisphere is in control of its own affairs, independent and self-governing. It implies a strong sense of autonomy and power.
The line uses a common metaphorical association of "house" with a nation or region, to create a vivid and impactful image of the hemisphere's determination.