わけにはいかない expresses that a person cannot do something because of responsibilities, social expectations, practical circumstances, or the consequences of doing it. It is stronger and more context-dependent than simply saying that something is difficult or impossible. With a verb in the negative form, V-ないわけにはいかない means that the person cannot avoid doing it, so it expresses a strong obligation or “must.” The form is commonly used when the speaker feels bound by the situation rather than by a formal rule.