Why did Solomon do that?

Solomon's brother Adonijah had tried to have himself made king with the help of Joab before Solomon was made king. The plan backfired & Solomon forgave his brother and sent him home.
But then Adonijah had Solomon's mother request to marry the young maid brought into King David to keep him warm on his deathbed (and no, David...he did not "know her" in the Biblical sense according to the Scriptures-for it tells us he didn't "know her").
But when Solomon was confronted with the request his reaction was - And king Solomon answered and said unto his mother, And why dost thou ask Abishag the Shunammite for Adonijah? ask for him the kingdom also; for he is mine elder brother; Now therefore, as the LORD liveth, which hath established me, and set me on the throne of David my father, and who hath made me an house, as he promised, Adonijah shall be put to death this day. 1 Kings 2:22,24

Matthew Henry, in his commentary, explains it well as to why Solomon reacted as he did: "To ask that he may succeed the king in his bed is, in effect, to ask that he may succeed him in his throne; The warrant is immediately signed for his execution, and no less a man than Benaiah, the son of Jehoiada, general of the army, is ordered to be the executioner, ...Solomon's wisdom did not see it needful to examine the matter any further; it was plain enough that Adonijah aimed at the crown, and Solomon could not be safe while he lived."