Several reasons:
1) Most people don't travel someplace without having accomodations made well ahead of time.
2) Most people don't just meet somebody online and then decide "okay, we'll come stay with you for a few days." How do you know the person you chose isn't a homicidal maniac? How do they know you two aren't sociopaths?
3) It sounds like a scam. This person invites you into their home, they leave for work, they come home to an empty or near empty house.