It's because the NPS rating numbers are ordinal, meaning that you can put the rating numbers in order, but the likelihood gap between the numbers may not be equal.
For example, 6 on the NPS scale would be less likely to recommend compared to 7 and 7 would be less likely than 8. However, the gap between 6 and 7 and the gap between 7 and 8 may not be equal. If you were to get the mean of 6, 7, and 8, you would get a value of 6, but there is no guarantee that the average of the participants' likelihood to recommend was actually equal to a 6.
For example, 6 on the NPS scale would be less likely to recommend compared to 7 and 7 would be less likely than 8. However, the gap between 6 and 7 and the gap between 7 and 8 may not be equal. If you were to get the mean of 6, 7, and 8, you would get a value of 6, but there is no guarantee that the average of the participants' likelihood to recommend was actually equal to a 6.
Measuring the mean would work if the interval between the numbers were equal. See here for details: https://en.wikipedia.org/wiki/Level_of_measurement