The short answer
Because they need almost the opposite conditions. Goldfish are cold-water fish, while most tropicals want a heated tank — set the temperature for one and you harm the other. On top of that, goldfish are large, messy and mouthy: they foul the water fast and will eat small fish. There’s no clever compromise that keeps both groups healthy, so the honest answer is to keep them apart.
The temperature clash
Goldfish do best around 18–22°C, whereas tropicals like tetras, guppies and gouramis want a steady 24–26°C. Warm the tank for the tropicals and the goldfish’s metabolism races, shortening its life and lowering its oxygen; cool it for the goldfish and the tropicals turn sluggish and disease-prone. Temperature isn’t a preference for these fish — it’s a health requirement, and their ranges barely overlap.
Waste and size
Even if you ignore temperature, goldfish are famously dirty. A single goldfish produces more ammonia than a whole school of small tropicals, and single-tails grow to 25–30 cm. In a shared tank they push nitrate up fast, destabilise the water, uproot plants and snap up any fish small enough to swallow. That’s a lot of stress for a delicate tropical community, and it forces bigger, more frequent water changes just to keep everyone alive. See what is a safe nitrate level?
What to do instead
Give goldfish their own cool, roomy, heavily filtered tank with other goldfish — a common goldfish or comet is better still in a pond. For a heated setup, build a proper tropical community with a betta, neon tetras or corydoras. Start at the aquariums hub and read can goldfish live with tropical fish? for the full picture.