The water conditions are too different. Gold fish like cold water. Betta like tropical, 78 or so, way too hot for a gold fish. Gold fish like high pH, Betta like neutral to low. Gold fish like high current, but that can terrorize the low/no current Betta. Same situation with aeration. Gold fish are a hard water fish, while Betta are a soft water fish. Basically, they have as different needs as they can get and still both be fresh water fish. You simply can't meet both of their needs in the same tank, it doesn't even get to the point where aggression is an issue.