سُبْحَانَ ٱللَّٰهِ
Holy Qur'an
Al-Qur'an
Kids Qur'an
I.e., on Muhammad, in order to "prove" that he is truly a bearer of God's message (a sceptical objection which resumes the theme enunciated in verses {1-2} and {15-17} above); see also 6:37 and {109} and the corresponding notes, especially note [94]. The pronoun "they" refers to both categories of deniers of the truth spoken of in the preceding passages: the atheists or agnostics "who do not believe that they are destined to meet God", as well as those who, while believing in God, "ascribe a share in His divinity" to all manner of imaginary intercessors or mediators (see verse {18} above).
This answer relates not merely to the question as to why God has not bestowed on Muhammad a "miraculous sign" of his prophethood, but also to the "why" of his having been chosen for his prophetic mission. See in this connection 2:105 ("God singles out for His grace whom He wills") and {3:73-74} ("God is infinite, all-knowing, singling out for His grace whom He wills").
Their demand for a Sign is disingenuous. All nature and revelation furnishes them with incontestable Signs. What they want is the Book of the Unseen opened out to them like the physical leaves of a book. But they forget that a physical Book is on a wholly different plane from Allah's Mysteries, and that their physical natures cannot apprehend the mysteries. They must wait. Truth will also wait. But the waiting in the two cases is in quite different senses. Cf. vi. 158 and ix. 52.