Why does a grandfather consider his male grandchildren to be the primary ones, and that he is obliged to spend on them, while his female grandchildren are not, and is there any basis for this in Islam?

A man's grandchildren through his male children are his 'asabah (agnatic relatives), and he is their ascendant, unlike his grandchildren through his daughters. Daughters' children are uterine relatives whose ties of kinship must be maintained. As for the obligation to financially support daughters' children when they are in need, there is a difference of opinion among scholars: In the Hanafi school, maintenance is obligatory for every mahram (unmarriageable) uterine relative. In the Maliki school, there is no obligation to support a son's child or a daughter's child. In the Shafi'i school, maintenance is obligatory for whoever is truly or figuratively called a father or mother. In the Hanbali school, maintenance is obligatory for parents and children, as well as grandparents and grandchildren, and for them, there is no distinction between an heir and a non-heir.