Winston despises Julia early in Part One of 1984—before he even knows her name—for a number of reasons. He hates her because he hates all young women who are Party members. With their sashes and emblems, Winston labels these young and pretty women as the most "bigoted adherents" of the Party, and this creates an immediate conflict between himself and Julia.
In addition, Winston also hates Julia because he thinks she might be a Party spy or agent of the Thought Police. He has this impression because she once passed him in a corridor and slipped him a "glance" which filled him with "terror." While he admits she is unlikely to be a spy, Winston cannot get past the sense of "uneasiness" she inspires in him.
Finally, Winston despises Julia as a way of demonstrating how easy it is to transfer negative feelings during the Two Minutes Hate. Instead of hating Emmanuel Goldstein, for instance, Winston sits in the cinema and imagines committing all sorts of atrocities on Julia's body, like tying her to a stake and shooting her with arrows.
These feelings toward Julia, however, quickly disappear once Winston realizes she is in love with him.