In being proud of your kids you are beaming on them for their successes and merits. It’s an uplifting pride because it puts the child in a place of honor in your heart and mind and conversation. You are uplifting them because you think they’re great and are pleased in them.
Being proud because of your kids, though, is not aimed at your kids at all. It’s self-focused. It’s feeling an increased sense of self because your child had a success. It’s a game of compare and contrast with other parents in which your child has become the basis for your success (or failure). It’s usury.
The principal holds true in any situation: work, creative expression, ministry, anything. Are you proud of the fruit of your efforts because it has merit and it is good? Or are you proud because of your efforts and want others to think you have merit and youare good?