Reasons for me:
Starbucks is a force of centralization and monopolization of commodity production. Anarchists generally look to decentralization as a model of social organization. Hence, Starbucks epitomizes one aspect of inherent opposition to anarchist goals.
When it began its empire in Seattle, Starbucks crowded out local, independent coffee houses (including several that were apparently run by some radicals/anarchists) by offering lower prices like other big box stores. Not that I am calling for more local independent capitalist enterprises, but there's definitely something to be said for having a more personal relationship with people who offer goods and services in your neighborhood.
Starbucks does not in fact pay their grunt workers well, but they do extend plenty of perks to managers, increasing the division of former co-workers into those who don't really care who signs their paychecks and company loyalists. Any business model that promotes disunity among proles is inherently opposed to anarchist goals.
Starbucks, as a centralizing/monopolizing enterprise, represents one very visible prong of the drive of American cultural homogenization domestically, and American cultural colonialism abroad. It's the Coca Cola of the late-20th century. Because setting up a Starbucks franchise is cheaper than McDonald's or Target, it can quite easily be considered the opening salvo in the extension of US capitalist expansion and eventual domination of just about anywhere.
Combined with Rice Boy's observations, does that provide you with a few credible answers?