The character of gas flow in the airways is governed by the Reynolds number, $Re = \dfrac{D\,v\,d}{V}$, where $D$ is the tube diameter, $v$ the mean velocity, $d$ the gas density and $V$ the viscosity. Turbulence appears when $Re$ is high (above roughly 3000), whereas flow stays smooth and laminar when $Re$ is low (below about 2000).
To decide why small airways are laminar, examine which variable in the equation is driven down. The key fact is geometric: although a single terminal bronchiole is narrow, there are millions of them in parallel, so their combined cross-sectional area is enormous, dwarfing that of the trachea.
Flow velocity is inversely related to total cross-sectional area, so as inspired air spreads into this vast parallel network its linear velocity collapses to very low values. Plugging a small $v$ into the Reynolds expression produces a small $Re$, and a small $Re$ means laminar flow.
This also exposes the wrong options: laminar flow requires a low (not high) Reynolds number, and the total cross-sectional area of the small airways is large rather than low. The genuine reason is the extremely low linear velocity of airflow in the small airways.
\[\boxed{\text{Linear velocity of airflow in small airways is extremely low}}\]