Please take a look at the following argument from an LSAT:
We know that there can be no obligation to an entity unless that entity has a corresponding right. Therefore, if we have no obligation towards an entity, that entity has no rights.
I vaguely sensed there is a difference between "an obligation to X" and "an obligation towards X". (Let X be an entity.) 'To' suggests a more direct relation than 'towards', which can mean concerning or in the direction of.
But is there any case that I have no obligation towards X, but then I still have an obligation to X?