Consider an ordered Categorical with missing values:

In [32]: cat = pd.Categorical(['a', np.nan, 'b', 'a'], ordered=True)

In [33]: cat.min()
Out[33]: nan

In [34]: cat.max()
Out[34]: 'b'

In [35]: cat.min(numeric_only=True)
Out[35]: 'a'

In [36]: cat.max(numeric_only=True)
Out[36]: 'b'

In [37]: cat.min(numeric_only=False)
Out[37]: nan

In [38]: cat.max(numeric_only=False)
Out[38]: 'b'

So from the observation above (and from the code:

This struck me as strange, for the following reasons:

• The fact that -1 is used as the code for missing data is rather an implementation detail, but now actually determines min/max behaviour (missing value is always the minimum, but never the maximum, unless there are only missing values)

• This behaviour is different than the default for other data types in pandas, which is skipping missing values by default:

  In [1]: s = pd.Series([1, np.nan, 2, 1])  
  
  In [2]: s.min()
  Out[2]: 1.0
  
  In [3]: s.astype(pd.CategoricalDtype(ordered=True)).min()
  Out[3]: nan
  
  In [5]: s.min(skipna=False)
  Out[5]: nan
  

• The keyword in pandas to determine whether NaNs should be skipped or not for reductions is skipna=True/False, not numeric_only (this also means the skipna keyword for categorical series is broken / has no effect).
  Apart from that, the name "numeric_only" is also strange to me to mean this (and is also not documented).

• The numeric_only keyword in reductions methods of DataFrame actually means something entirely different: should full columns be excluded from the result based on their dtype.

  In [63]: cat = pd.Categorical(['a', np.nan, 'b', 'a'], ordered=True)
  
  In [64]: pd.Series(cat).min(numeric_only=True)
  Out[64]: 'a'
  
  In [65]: pd.DataFrame({'cat': cat}).min(numeric_only=True)
  Out[65]: Series([], dtype: float64)
  

From the above list, I don't see a good reason for having numeric_only=False as 1) the default behaviour and 2) altogether as an option (instead of skipna). But it seems this was implemented rather from the beginning that Categoricals were introduced.

Am I missing something?
Is there a reason we don't skip NaNs by default for Categorical?

Would it be an idea to deprecate numeric_only in favor of skipna and deprecate the default?

cc @jreback @jankatins