When Proteus falls in love with Silvia, he decides that he's got to have her, even though his best friend is in love with her. His willingness to lie to his best bud and his relentless pursuit of Silvia (including his attempt to rape her) are major threats to the friendship.
If we think of male friendship as the play's "protagonist," then it sort of follows that romance acts as an antagonist to that relationship. Proteus's love for Julia causes Proteus and Valentine to be separated (Proteus stays behind in Verona instead of travelling with his pal). Proteus and Valentine also fall for the same girl, Silvia, who comes between them. Is it fair to blame Silvia for Valentine and Proteus's problems? Absolutely not, but the play suggests that romantic relationships with women have the potential to breakup male friendships.
OK, if romance is the protagonist you're rooting for, then you're probably thinking Proteus is a major "antagonist," right? He's the one, after all, who chases after Silvia when she's dating his best friend and tries to rape her. This could definitely work because he's one of the major obstacles in the way of Valentine and Silvia's hook-up.
The Duke of Milan is another "antagonist" to romance, don't you think? He is the guy who banishes Valentine from Milan and prevents him from physically being with Silvia, no?