Learn English – a word or expression to describe a person as entertainment to pass the time

Someone like you described could be feigning indifference (though this can also be used for a variety of reasons such as feigning indifference to being snubbed, being the subject of gossip, etc.):

feign /feɪn/ vb

1. to put on a show of (a quality or emotion); pretend: to feign innocence

2. (transitive) to make up; invent: to feign an excuse

3. (transitive) to copy; imitate

Etymology: 13th Century: from Old French feindre to pretend, from Latin fingere to form, shape, invent

indifference /ɪnˈdɪfrəns -fərəns/ n

1. the fact or state of being indifferent; lack of care or concern

2. lack of quality; mediocrity

3. lack of importance; insignificance

In English, to take someone to task means to reprimand them, that is, to criticize their failure of responsibility, which seems fairly close to the German usage, at least in the discomfort to the reprimanded party. But it doesn't necessarily contain the sense of asking for justification. For that you have to demand an explanation.

When you want to make somebody do something, you assign or give a task to him.

"Take" has a general meaning of seize or hold, and the OED records an old usage from 1250 of "take someone" meaning the modern locution of "take someone to task." Three hundred years later, "take someone to task" had the meaning of assign someone a task, but some time after the 1650s, this usage become obsolete, superseded by the old ancient meaning of reprimand.