In the Shafi’i Madhhab, if a woman’s son is connected to her only by the bond of being her child, then he cannot act as her guardian and marry her off. If another connection between them is established, then he may according to that. An example of this is them sharing in lineage by him being both her son and also the son of her uncle’s son; or for example, if he was the judge [qadi].
The right of wilayah [guardianship] is one established by nasab [lineage], and a woman’s lineage goes back to her father and his family; while her son’s lineage is traced through his father.
This is the Shafi’i Madhhab’s position on the matter, the other 3 Schools and Imam Shafi’s student, Imam Muzani, maintained that a woman’s son may act as her wali.
(See: Mughni al-Muhtaj 4/249; Rawdat al-Talibin 5/381)