Final answer:
The 'irony of fate' that W. E. B. Du Bois refers to is the American imperialist expansion in the Caribbean and the Pacific Ocean, which hampered efforts of Black Americans seeking to emigrate to escape domestic racism and discrimination.
Step-by-step explanation:
The "irony of fate" that W. E. B. Du Bois points out, which made the alternative of emigration hopeless for those seeking to escape racism and discrimination in America, is associated with American imperialist expansion in the Caribbean and the Pacific Ocean. Du Bois indicated that simply fleeing to different geographies would not suffice as the United States' own imperial interests followed these individuals abroad, undermining the notion of finding refuge. Moreover, Du Bois, within his seminal work 'The Souls of Black Folk', critiqued the existing power structures and highlighted the perils that Black Americans faced due to systemic injustices and discriminatory practices perpetuated within and by their own nation.
Through the lens of his sociological and political activism, he noted that while Black Americans served internationally in wars, expecting a post-war era of improved civil rights, the domestic reality upon their return reflected an unchanged or even worsened stance on racial equality by white Americans. This persistence of the status quo suggested that geographical escape would not resolve the deep-rooted issues of racial discrimination, as the challenges faced were integral to the American society and extended beyond its borders through the reach of its imperial ventures.