I tried the fix that Jamie suggested and it does eliminate the error. However I don't think it explains why training on a subset of the training data also works even though the subset contains even fewer unique values.

Convert to numeric

classifier = Classify[N[training]]
classifier[testing]

All testing samples are classified as P, is that expected?

"P", "P", "P", "P", "P", "P", "P"}

The probabilities for P and NP are extremely close for most of the samples.

classifier[testing, "Probabilities"] // Column

{
 {<|"NP" -> 0.496296, "P" -> 0.503704|>},
 {<|"NP" -> 0.486345, "P" -> 0.513655|>},
 {<|"NP" -> 0.499325, "P" -> 0.500675|>},
 {<|"NP" -> 0.494909, "P" -> 0.505091|>},
 {<|"NP" -> 0.492273, "P" -> 0.507727|>},
 {<|"NP" -> 0.480284, "P" -> 0.519716|>},
 {<|"NP" -> 0.458435, "P" -> 0.541565|>}
} 

I tried several of the available classification methods to see how much the results varied

methods = {"DecisionTree", "GradientBoostedTrees", 
   "LogisticRegression", "NaiveBayes", "NearestNeighbors", 
   "NeuralNetwork", "RandomForest", "SupportVectorMachine"};

classifiers = Map[{#, Classify[N[training], Method -> #]} &, methods];

Map[First[#] -> Last[#][testing] &, classifiers] // Column

Gives

{
 {"DecisionTree" -> {"NP", "NP", "NP", "P", "NP", "NP", "P"}},
 {"GradientBoostedTrees" -> {"P", "P", "NP", "NP", "NP", "P", "NP"}},
 {"LogisticRegression" -> {"P", "P", "P", "P", "P", "P", "P"}},
 {"NaiveBayes" -> {"NP", "P", "NP", "NP", "NP", "P", "P"}},
 {"NearestNeighbors" -> {"NP", "NP", "NP", "NP", "NP", "NP", "NP"}},
 {"NeuralNetwork" -> {"P", "P", "P", "NP", "P", "P", "P"}},
 {"RandomForest" -> {"NP", "NP", "NP", "NP", "NP", "NP", "NP"}},
 {"SupportVectorMachine" -> {"NP", "NP", "NP", "NP", "NP", "NP", "NP"}}
}

Without knowing the details of what this data represents it is hard to know which method is most appropriate.

That definitely sounds like the same problem. I will work with it some tomorrow. Thanks for pointing this out Jim.

Thank you for working on this Rohit. Jim posted a link to a potential fix below. It sounds like more of a work around but it might work. I am going to work with it some tomorrow.

I cannot reproduce this on 11.3.0 for Mac OS X.

nn[TestData]
{"B", "B"}

Note that in the code you posted, both TrainingData and TestData are missing an opening {.