I am trying to use Zonal Statistics to find the most common value of a high-resolution classification within a coarser fishnet grid (10x10 m). The idea is to use this high-res classification as training data for a classification using Sentinel 2 data. 
The fishnet was made using the Sentinel 2 data as a template and then rasterized. All raster operations (e.g. rasterizing the high-res classification, which was vector data) have used this fishnet raster as a snap raster. However, when I use Zonal Statistics (Statistics Type: Majority) to find this most common value, I get wrong results. For example, a cell which has only a small percentage of 'Brown' (small dump hill) values is assigned as having a majority of 'Brown' cells (see screenshot). 
For this Zonal Statistics operation, I used the Sentinel cell size (10 m). When I use the cell size of the original classification (~2.3 cm), I do get the expected results ('Yellow', which is bare ground) (see screenshot below), but then I get way too many cells, which is a problem for further operations (the screenshot below seems like it has a coarse cell size, but these are actually millions of small (2.3 cm) cells.
How is it possible that ArcGIS Pro assigns a 'Brown' value to a cell which barely any 'Brown' in it? And why does this not happen in all cells that have small amounts of 'Brown' in them? Should I not use the Sentinel cell size as output cell size for Zonal Statistics?
