Why is this girl I kindof like playing tug of war with me showing interest one day and none the next?
"Kind of like"? If you only "kind of like" her, it sounds like you and this girl are playing similar flirtation games with each other. A little interest, peeking to see the reaction, etc. Depending on your ages and experience with relationships, this could be normal -- like in high school or college. People might do this when initially trying to figure out if the other "likes" them -- inconsistent until "sure.".
Why? This is a difficult to answer question , and may be u have to have a serious talk with her .
Dunno til you ask. Tell her how you feel when she does that, & focus on yourself and your feelings or she may become defensive or just shut down. You may feel rejected or unwanted because she doesn't show interest. Physical contact is important to any intimate relationship. Ask her if everything is ok. Maybe she is depressed or has low self esteem. Keep an open line of communication.
Girl's nature. Not uncommon with girls. The question is do you want to play this game with her? You can do the same.