come around
To slowly change your mind and finally agree with something.
To come around means to change your mind about something, especially when you initially disagreed or resisted. When your friend finally comes around to your idea for a weekend activity, she's decided you were right after all. When a skeptical teacher comes around to trying a new teaching method, he's reconsidered his doubts.
The phrase captures that gradual shift from “no” to “yes,” from doubt to acceptance. It might take days of patient explanation before your parents come around to letting you adopt a pet. A stubborn teammate might not come around to a new strategy until she sees it working.
People often come around after seeing new evidence, experiencing something themselves, or simply having time to think. A classmate who insisted your science fair project wouldn't work might come around when your experiment succeeds.
The phrase can also mean to visit someone, usually casually: “Come around to my house this weekend.” It can also describe regaining consciousness after fainting: “After a few minutes, she came around.” But the most common meaning involves that satisfying moment when someone finally agrees with you after initially saying no.