I am just studying Hypothesis Testing for Difference between Two Population Mean
Here, I found that the Null Hypothesis is assumed that, the mean value of the both populations are same (i.e $\mu_1 = \mu_2$)
Why it doesn't assume that the mean values are unequal?
Can I state in null hypothesis that they are unequal and prove it by the same process??
I know it's a very silly question
But any help is much appreciated
One thing to note is that you never prove or disprove the null hypothesis. You can reject it or fail to reject it.
There are a number of reasons why the null hypothesis is stated as $H_0:\mu_1=\mu_2$. One reason is that the null/alternative hypotheses are not symmetric. Let $H_0$ and $H_A$ be the null and alternative hypotheses, respectively. Let $Y$ be your observed outcome. Then you will reject the null hypothesis if $\mathbb{P}(Y|H_0)$ is very small (that is, the probability of observing the outcome that you observed is very small when the null hypothesis is true). If you reverse the null/alternative hypotheses, then $H_A$ would be the "new" null hypothesis, and you would reject $H_A$ if $\mathbb{P}(Y|H_A)$ is very small. In effect, you would be switching the burden of proof. Rather than needing strong evidence to reject $H_0$ in favor of $H_A$, you would need strong evidence to reject $H_A$ in favor of $H_0$. This explains why you cannot flip $H_0$ and $H_A$ and end up in a symmetric position.
Generally speaking, null hypotheses tend to assume there are no differences unless strong evidence suggests that there are differences (ie assume $\mu_0=\mu_1$ until there is strong evidence otherwise). You could argue that this is arbitrary, but it is typically the way things are done. It does have one benefit: When two models are basically equivalent in terms of performance, you prefer the simpler one. And the model with $\mu_0=\mu_1$ is simpler than the model with $\mu_0\neq \mu_1$, since it needs only one parameter ($\mu_0=\mu_1$) instead of two ($\mu_0, \mu_1$). So framing the null hypothesis as: One or more parameters are equal (or, one or more differences between parameters are $0$) will result in a simpler model when you fail to reject the null hypothesis. So when framed in this way, it takes strong evidence for you to choose the more complex model. If you switch the null and alternative hypotheses, you will have the more complex model unless there is strong evidence to reject it in favor of the simpler model.
Last, in this particular example, it is very easy to calculate $\mathbb{P}(Y|\mu_0=\mu_1)$. You get a test statistic with a known distribution. But the condition $\mu_0\neq \mu_1$ does not yield a test statistic with a known distribution, because it contains many possibilities: $\mu_0=\mu_1+1$, $\mu_0=\mu_1-1$, $\mu_0=\mu_1+10.3$, $\mu_0=\mu_1+.00000001$, etc. In this case, it is easy to calculate $\mathbb{P}(Y|\mu_0=\mu_1)$. How would you calculate $\mathbb{P}(Y|\mu_0\neq \mu_1)$?