I'm not sure if you ever figured this out but I was trying to find answers on this exact same question and there aren't really any good answers in my opinion. I finally figured it out though. OrdinalEncoder is capable of encoding multiple columns in a dataframe. So, when you instantiate OrdinalEncoder(), you give the categories parameter a list of lists:

enc = OrdinalEncoder(categories=[list_of_values_cat1, list_of_values_cat2, etc])

Specifically, in your example above, you would just put ['low', 'med', 'high'] inside another list:

end = OrdinalEncoder(categories=[['low', 'med', 'high']])
enc.fit_transform(X.loc[:,['animals']])
>>array([[0.],
         [1.],
         [0.],
         [2.],
         [0.],
         [2.]])
# Now 'low' is correctly mapped to 0, 'med' to 1, and 'high' to 2

To see how you can encode multiple columns with their own individual ordinal values, try this:

# Sample dataframe with 2 ordinal categorical columns: 'temp' and 'place'
categorical_df = pd.DataFrame({'my_id': ['101', '102', '103', '104'],
                               'temp': ['hot', 'warm', 'cool', 'cold'], 
                               'place': ['third', 'second', 'first', 'second']})

# In the 'temp' column, I want 'cold' to be 0, 'cool' to be 1, 'warm' to be 2, and 'hot' to be 3
# In the 'place' column, I want 'first' to be 0, 'second' to be 1, and 'third' to be 2
temp_categories = ['cold', 'cool', 'warm', 'hot']
place_categories = ['first', 'second', 'third']

# Now, when you instantiate the encoder, both of these lists go in one big categories list:
encoder = OrdinalEncoder(categories=[temp_categories, place_categories])

encoder.fit_transform(categorical_df[['temp', 'place']])
>>array([[3., 2.],
         [2., 1.],
         [1., 0.],
         [0., 1.]])

You were almost there !

Basically the fit method, prepare the encoder (fit on your data i.e. prepare the mapping) but don't transform the data.

You have to call transform to transform the data , or use fit_transform which fit and transform the same data.

enc = OrdinalEncoder()
enc.fit(df[["Sex","Blood", "Study"]])
df[["Sex","Blood", "Study"]] = enc.transform(df[["Sex","Blood", "Study"]])

or directly

enc = OrdinalEncoder()
df[["Sex","Blood", "Study"]] = enc.fit_transform(df[["Sex","Blood", "Study"]])

Note: The values won't be the one that you provided, since internally the fit method use numpy.unique which gives result sorted in alphabetic order and not by order of appearance.

As you can see from enc.categories_

[array(['F', 'M'], dtype=object),
 array(['A', 'AB', 'B', 'O'], dtype=object),
 array(['Biology', 'English', 'Math', 'Science'], dtype=object)]```

Each value in the array is encoded by it's position. (F will be encoded as 0 , M as 1)

OrdinalEncoder has a categories parameter which accepts a list of arrays of categories. Here is a code example:

from sklearn.preprocessing import OrdinalEncoder
enc = OrdinalEncoder(categories=[['first','second','third','forth']])
X = [['third'], ['second'], ['first']]
enc.fit(X)
print(enc.transform([['second'], ['first'], ['third'],['forth']]))