There are alternate points of view. Rice could go to Arsenal and instantly be part of the spine along with Odegaard, Saka, Martinelli, Saliba (all of which are under 24). Rice could come to Arsenal and instantly be part of the core as a place will be made for him in his preferred position. We are investing beyond Rice and keeping our players. Arteta is a young manager in the infancy of his Arsenal tenure and is likely to stay for a long time. If Rice joined Man City and signed a 5 year deal, who will be his manager in years 3-4-5? Pep is winding down at City and has likely signed his last contract. There is also a cloud that looms over Man City that could become a storm. Plus there is the London factor and home comfort.
Not every road points to Man City.