If we imagine blue as labelling the odd numbered segments and green as labelling the even numbered segments, it is clear that there must be an even number of segments in total. The number of gaps between segments is equal to the number of segments minus 1, so it is odd.
Here’s a more conceptual framing:
If we imagine blue as labelling the odd numbered segments and green as labelling the even numbered segments, it is clear that there must be an even number of segments in total. The number of gaps between segments is equal to the number of segments minus 1, so it is odd.