1. An uneven number of boys wanted to play the game, so that when both teams had chosen the same number of players, one boy was left standing in the middle. John was the odd man out.
2. I felt as though I didn’t belong with the group of people at the party. I was odd man out.

The expression probably originates from the idea of choosing up two sides for a game in which both teams need an even number of players. If there were an uneven number of people wanting to play, the last (odd) person was left out. The expression has broadened in its meaning to describe anyone who is not included or made to feel part of a group. When the expression is used to describe a woman, the word “man” does not become “woman”.