Hah! Of course freedom and equality oppose each other.
Look, in order to create a perfectly even(equal) wealth distribution in this country, a large number of regulations would be required(regulations that inherently invade on your freedoms).
On the other hand, if we make no effort to maintain equality against individual will, then what will immediately begin is a predatory, Darwinian game in which winners crush losers, and the sly horde riches stolen from the naive.
Not very equal.
There's a silly joke that demonstrates how freedom and equality oppose each other. At HomestarRunner.com, there was a clip in which Marzipan was teaching a kindergarten class, and she only gave her students crayons that couldn't write, reasoning that it would prevent any one student from artistically outshining the others.
Do you see how this absurd situation examplifies my point?
The freedom to pursue anything better or do anything greater than anyone else automatically creates inequality.
Justice is seperate, too, because it encrouages the idea the people should be forcably punished or rewarded on merrits. This idea conflicts with both freedom and equality.