There are divergent views about the challenge of Jesus in Mk 10:21. Some exegetes affirm that everything has to be given up to follow Jesus; for others, this is impractical. The former is presented as Position A; the latter, Position B. In addition, others are not in agreement about the addressee of the challenge of Jesus; that is, whether or not it is for everyone. In line with these contrary views, the thesis then asks the question, ‘Does Jesus demand to give up everything from everyone to follow him’? This is answered in two ways: presentation of selected commentaries and articles about the two positions and exegesis of the story of the rich man in Mk 10:17-31. The former identifies the two positions as presented by respected scholars. The latter indicates whether or not the positions are correct. Subsequently, within the text, which is divided into three sections, it is found that Positions A and B are present. At one point, Position A is either correct or wrong. The same is true with Position B. However, outside the text, Position B is affirmed as correct. Despite these seemingly conflicting positions, the answer to the main question is still drawn. After further analysis, most probably, it is reckoned that, Yes, Jesus demands to give up everything that hinders one from following Him. This can be in the form of possessions, families, professions or anything. This is addressed to anyone. With this finding, the thesis hopefully contributes something to the understanding of the challenging demand of Jesus.