There are 2 main definitions of score points in English:

score points1

Deliberately make oneself appear superior to someone else by making clever remarks: she was constantly trying to think of ways to score points off him
See parent entry: point

Definition of score points in:

There are 2 main definitions of score points in English:

score points2

Outdo another person, especially in an argument: politicians are always sniping at one another to score party points the participants seemed more eager to score points off one another than to explain the social phenomena under investigation
See parent entry: score

Definition of score points in: