I have the following data where for each column, the rows with numbers are the input and the letter is the output.
A,A,A,B,B,B
-0.979090189,0.338819904,-0.253746
I think your model does not get trained properly and because it only has to guess one value it doesn't get it right. May I suggest switching to KFold or StratifiedKFold. LOO has the disadvantage that for large samples it becomes extemely time consuming. Here is what happened when I implemented StratifiedKFold with 3 splits on your X data. I have randomly filled y with 0 and 1, instead of using A and B and have not trasposed the data so it has 12 rows:
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import accuracy_score
from sklearn.metrics import confusion_matrix
from sklearn.model_selection import StratifiedKFold
import pandas as pd
csv = 'C:\df_low_X.csv'
df = pd.read_csv(csv, header=None)
print(df)
X = df.iloc[:, :-1].values
y = df.iloc[:, -1].values
clf = KNeighborsClassifier()
kf = StratifiedKFold(n_splits = 3)
ac = []
cm = []
for train_index, test_index in kf.split(X,y):
X_train, X_test = X[train_index], X[test_index]
y_train, y_test = y[train_index], y[test_index]
print(X_train, X_test)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
ac.append(accuracy_score(y_test, y_pred))
cm.append(confusion_matrix(y_test, y_pred))
print(ac)
print(cm)
# ac
[0.25, 0.75, 0.5]
# cm
[array([[1, 1],
[2, 0]], dtype=int64),
array([[1, 1],
[0, 2]], dtype=int64),
array([[0, 2],
[0, 2]], dtype=int64)]