I would suggest that holding feelings or emotions against people is kind of awkward. You might hold other things against them, which could lead to certain feelings towards them. For example, one could hold another's sloppy eating habits against them, which could easily develop into an overall feeling of negativity towards that person.
In its most basic form, it describes opposition to something. The opposing element could literally be physical, such as a push backwards, or the philosophical opposition found in the form of a contrary ideology. This is in contrast to toward, which basically describes directional movement nearer to something or someone. There is no implication of good or bad contained within.
@fumble, the provided financial examples are somewhat interchangeable because they concern either applying funds against (in opposition to, negating) an amount due or applying funds toward (in the direction of) that same debt. In he first example, you're acting against the debt itself; in the second, you're acting against the account which holds the debt. Splitting hairs here.
In the example of rebel forces, I must assert that moving toward a place does not imply active conflict; they're going there, but not necessarily fighting anybody there. Moving against a city, however, certainly does imply fighting.