After the Communist invasion, the USSR ruled in Afghanistan from 1978 - 1989. At the time, it must have made all kinds of sense (from the Soviet point of view) to take over Afganistan. When you look at this map, the USSR was right there.
Virtually all the neighboring countries were part of the Soviet republic. (Look at the lower left corner of that map - Afg. is Afghanistan. Other than Iran to the west and China to the east, the USSR was it. I'm sure the USSR truly believed they were protecting Afghanistan from the improper advances of those other countries.
What it meant for Laila, attending school under the Soviet regime, was she was taught to believe there was no difference between men and women, and everyone should receive equal treatment.
Was that why she was feistier and less subservient to Rasheed than Mariam, later in the book?
Laila was also raised loathing the Soviet invaders. As far as her family was concerned, the Soviets had murdered both her brothers.
Why was Laila so different than Mariam? Was it because of her parents' attitudes? Mariam's schooling under the Soviets? Or was it just a difference of personality?