There really is no reason to think Ashi is Jack's daughter. No evidence or clues have been given to suggest such a thing, I just like the idea. I don't know why others came to that conclusion, but my thinking was that Ashi's mother conceived her children with Jack because it was the only way to create warriors that could match the legendary samurai. This is kind of a reverse of the "hero is a descendant of the villain" cliche and I thought Tartakovsky could have some fun with it.



As for how it could happen, the high priestess of Aku would lie to Jack about who she was, obviously. Maybe she would pretend to be a damsel in distress and have Jack protect her until she got what she wanted, or maybe she would just get him drunk at some bar like a one-night-stand, or maybe she was inseminated with artificial sperm grown from blood cultures collected from one of Jack's battles. There are literally dozens of possible explanations and it doesn't take much imagination to think of one. You just have to willing to explore the possibility.



As for love, what Jack and Ashi found last episode was not love, it was sex. Love and sex are not the same thing. Confusing the two concepts always leads to disaster. Sex also does not equal happiness, another misconception that can lead to disaster.



Anyways, one last reason why I liked the idea of Ashi being Jack's daughter is that I thought that she would serve as his heir, ruling the future world once Aku is destroyed and Jack has gone back to the past.