There are laws and acts to guarantee equal opportunity. For example, the Equal Pay Act of 1963 which requires equal pay for equal work and the Civil Rights Act of 1964 which prohibits discrimination in programs receiving Federal funds. But on a more personal level, we don't all start at the same line. While every American can be denied almost nothing because of race, color, national origin, religion, sex, familial status, or disability, a lot of Americans aren't in the position to be discriminated against. This means that many Americans do not have the opportunity to fully exercise their liberty.
Personal liberty is freedom.
It means all persons must be given the opportunity to realize their own goals. It translates to self-determination. The Constitution states all people have the right to life, liberty and freedom. This is a bit idealistic because one person's liberty may infringe upon another person's freedom. Take abortion for example.