* Electronegativity: Oxygen (3.44) is more electronegative than fluorine (3.98). This means fluorine has a stronger pull on electrons than oxygen. In an ionic bond, the electronegativity difference is large enough for one atom to completely "steal" an electron from the other.
* Sharing, not Stealing: Fluorine and oxygen are both highly electronegative nonmetals. When they bond, they share electrons in a covalent bond, forming a covalent compound, rather than transferring electrons to create ions. This sharing is unequal, with the fluorine atom attracting the shared electrons more strongly, creating a polar covalent bond.
In summary: Due to their similar electronegativity, fluorine and oxygen bond by sharing electrons in a covalent bond, not by transferring electrons to form an ionic bond.