Why did the Portuguese king refuse F. Magellan’s offer?

The answer here is very simple. The Portuguese king believed (however, like most at that time) that the earth was flat, and from Magellan invited him to travel around the world, thanks to which new trade routes could open, but the king could not accept such an opinion that the earth was not flat, but hence, he could not agree with Magellan’s proposal either. Therefore, Magellan had no choice but to follow in the footsteps of Columbus and go into the service of the Spanish king.