Why my fan oven is taking soo long to cook chicken?

I ‘m afraid, but it seems you misunderstood something here. A fan oven is not a wonder tool that will mysteriously cook a meal in super short time. (That would be partially correct for a microwave or microwave/convection combination.) Even the article you linked to doesn’t give 15 minutes, but 18-20 minutes per pound plus another 20 minutes on top.

Yes, cooking times can, but need not in all cases, be somewhat shorter, and reducing the temperature compensates the improved heat transfer due to the fan to prevent preliminary browning. But apart from that, the difference to a non-fan oven isn’t that much.

But a word of warning re. relying on cooking times to judge doneness of a roast: Don’t. Yes, a timing table may be useful for a ballpark number, but every oven is different, the starting temperature of the meat may differ, geometry is a factor and even the breed and form of raising of the animals can have an influence. A meat thermometer will be the only way to precisely determine the core temperature and hence doneness and, even more important, food safety. From your post, it seems you did use common sense (and maybe a thermometer), but for future readers I would like to add this note.