No horse in this race phrase informal
No vested interest in the outcome of something, usually a contest or debate
Don't ask me about the contest. I had no horse in this race.
I have no horse in this race because whoever wins has nothing to do with me.
Be outside the ability or willingness of someone to care more about a particular person or issue
How's it going?; how are you?
An individual should only work on and care about his or her work, and should not interfere with others.
If you like something very much or find something appealing or interesting to you, it strikes your fancy.