Why does Lena hate birds?

Boesman and Lena are forced to wander from place to place after their home has been bulldozed—a common practice in apartheid-era South Africa. Their enforced wanderings constitute a parody of the freedom enjoyed by birds: like birds, they can wander, but they cannot settle down in one place for any length of time.
That's why Lena resents the birds for possessing the freedom that, as a woman of color in South Africa, she is routinely denied. If a bird's nest is destroyed, it can always be rebuilt elsewhere. But Lena and Boesman can't do the same with their ruined shacks. The racist apartheid state dictates where they can and can't live, while the birds remain proverbially free to go wherever they like. The very presence of the birds acts upon Lena as a constant reminder of her complete lack of freedom. It's almost like the birds are taunting her as they fly overhead. Lena's hardscrabble existence is resolutely earthbound, but the birds have the freedom to soar high into the sky. It's little wonder, then, that Lena hates them so much.

Athol Fugard's Boesman and Lena is centered on a "coloured" couple living in South Africa during the era of Apartheid. The play was first performed in South Africa in 1969.
Near the beginning of act 1, we come to a brief moment where the stage directions describe Lena watching and yelling at a bird flying slowly out of her view. 
Essentially, Lena does not like birds because she is jealous of them, because they have a freedom that she does not. Birds can fly away, while she and Boesman have to stay on the ground, "in the mud." Lena cannot even choose where to stay on the ground. She and Boesman have to move from place to place, as white men keep bulldozing the shantytowns where homeless "coloured" people live, telling them to "Clear out!" She feels that the place they have come to is "rotten," but for now she has no choice but to stay there.