In the lecture of 1930 on "The Essence of Human Freedom", Heidegger introduces the enigmatic notion of "Angriff" (challenge). This paper aims to clarify this idea against the background of the wide semantic field of the verb greifen (to grasp). As a result of such analysis, "Angriff" can be interpreted as reflecting a new meaning of the notion of «mineness» ("Jemeinigkeit"), which is not perfectly compatible with the conceptual framework of fundamental ontology. The «turn» (Kehre) appears to be already at work.