Starfire is passionate, yet, she is pure. But...that doesn't run in the family. For she has a sister, something that the Teen Titans found out very early in the series, and unlike Starfire, she's anything but pure.
Blackfire is conceited, repeatedly bullies Starfire, makes her feel inferior, and much more. She's even tried to use her sister to get out of prison stints and even tried to force her hand in marriage to an alien race because of an "invasion" that she helped set up!
In the end, Starfire got her revenge, she usurped her sister for the throne of Tamaran, exiling her in the process. And then proved she was the better woman by abdicating the throne to someone more qualified. Like we said, Starfire is pure.