make (one's) point
To effectively communicate or explain one's opinion, idea, or point of view. A: "The early flight might be cheaper, but we won't enjoy our first day there because we'll be so tired!" B: "OK, you made your point. Let's book the later one instead." But Bob, if we don't secure the investment by Friday, we stand to lose everything the other investors have put in so far. Have I made my point?
make one's point
Effectively express one's idea, as in I see what you mean about skateboards being dangerous-you've made your point. This expression uses point in the sense of "an important or essential argument or suggestion." Also see make a point of; take one's point. [c. 1800]