An Alpha male is a leader and never follows. He will not chase a woman. She has to fit his agenda. The woman prefers a man that other women desire. She will actually get turned on by his cheating.
The Challenge of being in the race with potentially other women, providing that they are beautiful women and not thots.
Because he should never rely on her to complete him. No woman can do this.
To keep her curious. Women generally feel naturally wanted by all men, even if they only want to hit and run. So when a man shows no real thoughts of commitment she wonders.
To keep busy and to keep her waiting. Never give a woman all of your time, she would only abuse it and later lose respect for you.