Also in the footnote of the same section of Sahih Muslim it...

Also in the footnote of the same section of Sahih Muslim it is mentioned that Prophet possibly wanted to assign a Caliph on that Thursday, and the matter might have been the matter of successorship which caused such dispute. In fact, most of the people who where present there, understood the intention of prophet, the same as what Umar did.

Because prophet had previously indicated the issue when he said several times that: "I shall leave for you two precious Symbols: The book of Allah, and my progeny, that is…