Answer:
The Civil Rights Act of 1964 (Act) opened public facilities, public accommodations, education, jobs, and voting booths to more Americans by making it illegal to discriminate on the basis of race, color, religion, and national origin. Women, however, were glaringly absent. In fact, only the employment provisions of Title VII mention women at all—and that mention was inserted as a last-minute attempt to defeat the bill entirely rather than to include women in the civil rights revolution. Believing that even those in Congress who supported racial equality would balk at the idea of gender equality, Virginia Congressman Howard Smith submitted an amendment to add “sex” to the categories protected by Title VII. Fortunately, his ploy backfired when the few women in Congress supported the amendment and ensured its survival.
Despite this small victory, the Act still ignored women in education. Women were not included in Title VI, which made it illegal to discriminate in federally financed educational programs. Meanwhile, Title VII excluded educational institutions, local and state governments, and the federal government, meaning that these organizations could continue to discriminate against women at all levels. At the time, many secondary schools required girls to take home economics and English, while boys took industrial arts and calculus. Physical education classes were sex segregated, with boys playing team sports while girls engaged in calisthenics or tumbling. Athletics remained a male-only bastion, with girls relegated to cheering. Even the few states that offered athletic opportunities to girls subjected them to discriminatory rules like six-on-six half-court basketball or scheduled them in odd seasons so the boys would not have to share their facilities.
The discrimination continued in colleges and universities. Many schools completely barred women from stereotypically male programs like law and medicine. Still others set quotas that limited the number of female students, no matter their qualifications relative to male applicants and students. Many of the nation’s prestigious schools—including even public colleges like the University of Virginia—remained male only. Meanwhile, women in academia were denied tenure or simply not hired because of their gender. The law even allowed public schools to assign female teachers in elementary schools while they hired only males for high school math or science classes. Not even the Equal Protection Clause protects women from these indignities, because the Supreme Court has not yet recognized “sex” as a suspect class entitled to heightened scrutiny.
This constant refrain is meant to convey the powerful message that whatever happens to African-Americans, however many times they're subjected to racism, prejudice, and bigotry, they will never be kept down. They will always rise up and assert their identity in the face of those who would keep them in a state of permanent subjection.
"I rise" is intended as a message of hope and inspiration, an injunction to dig deep in the face of oppression, to stand tall and not be ashamed of one's identity. Most people are familiar with the expression of picking yourself up, dusting yourself off, and starting over again as a response to life's numerous setbacks. The same principle is in operation here.
The speaker seems to suggest that African-Americans will always be subjected to oppression of one sort or another. That being the case, there's only one way for African-Americans to maintain their dignity and sense of self-worth, and that's by rising up every time society tries to keep them down.