Electronegativity is an intrinsic property of the elements. So the reason that fluorine is more electronegative than oxygen is just because it is.
The "rule" that electronegativity increases towards the right and towards the top is more of a guideline. It is a generality that lets you compare within a single column or single row, but it doesn't tell you absolute values of electronegativities and is not too helpful for comparing elements that are not either in the same row or in the same column.
Here are the most important electronegativities to know:
Hydrogen - 2.20
Carbon - 2.55
Nitrogen 3.04
Chlorine 3.16
Oxygen 3.44
Fluorine 3.98
Don't memorize the numbers; just know that N, Cl, O, and F are very electronegative and that their electronegativities increase in that order. Also you need to know that C and H are not very electronegative and that their electronegativities are similar enough that a C-H bond is non-polar.