Why did sega make the game Shadow The Hedgehog

Various reasons. They did a poll, asking the question 'Which Sonic character should get his/her own spinoff?' and Shadow was the victor. Yuji Naka was interested in splitting Shadow from Sonic, to avoid the constant comparison to one another and to try and develop the character as a full character rather than just another cliched 'anti-Sonic'- a role that had been filled already by many characters, the most prominent being Metal Sonic. Shadow had a backstory from his last two console appearances, which could be expanded on, especially since he got amnesia. Sega cashed in on this mystery to make the game that we know today.