Confusion about 1- vs 2-tailed tests for feature selection by hypothesis testing 
Suppose $x_i\ (i=1,2,...,N)$ be attribute values for $N$ samples from
class $W_1$ with mean $\mu_1 $ and $y_i\ (i=1,2,...,N)$ be attribute
values for $N$ samples from class $W_2$ with mean $\mu_2 $.


For feature selection using hypothesis testing, why we should define $H_0 =\mu_1 -\mu_2=0 $

 A: This is one thought that $(B)$ is true:
You have two classes $Z=0, 1$ and usually we classify such that $P(Z=1| X) >0.5$. You need to choose a feature that increase the $P(Z=1|feature)$.
I think if you assume normality and use LDA (I mean assume variance of the features different  classes are equal), then you should be able to relate the problem to the mean of the features. I also think 2 is the only correct answer if you look at the problem this way.
Suppose $P(Z=1| feature) =$ a $\mu_{feature} + b$ with $a>0$. Then $P(Z=1|x) > P(Z=1|Y)$  if $\mu_x > \mu_y$.
A: Option B is false.
I'm assuming the purpose of feature selection is to identify predictors which help distinguish between classes.  Ostensibly, if two classes have an observed difference in class conditional expectation which is larger than what could reasonably happen under chance + test assumptions, then that predictor should be used to construct a model.
Assume that the sign of $\mu_1 - \mu_2$ did matter, and assume further that we would select feature $x$ because we reject the null of the test.  The labels of the classes are arbitrary, so permute them switching $W_1$ to $W_2$ and vice versa.  It is important to stress that nothing changes about the data itself, only the class labels.
Under this permutation, the sign of $\mu_1 - \mu_2$ would flip, and we would fail to reject the null and hence not select $x$ as a feature.  That isn't a desirable property of the procedure.  What features we select should not depend on arbitrary labels.
Its very clear here that your TA has made an error, and if the TA is insistent they are correct then they would have to deal with the dilemma I've outlined here: either the procedure depends on arbitrary labels, or the sign of the difference is irrelevant (unless we've made it relevant, in which case the question here is moot and the exam question is to blame).
You've already provided a reputable source, so I don't think additional sources are needed.  You're right, the answer should be A.
