Rejecting $H_0$ requires your study to have enough statistical power. If you're able to reject $H_0$, you can say that you have gathered sufficient data to draw a conclusion.

On the other hand, not rejecting $H_0$ doesn't require any data at all, since it's assumed to be true by default. So, if your study doesn't reject $H_0$, it's impossible to tell whether $H_0$ is true, or your study simply wasn't large enough.

Rejecting $H_0$ requires your study to have enough statistical power. If you're able to reject $H_0$, you can say that you have gathered sufficient data to draw a conclusion.

On the other hand, not rejecting $H_0$ doesn't require any data at all, since it's assumed to be true by default. So, if your study doesn't reject $H_0$, it's impossible to tell which is more probable: $H_0$ is true, or your study simply wasn't large enough.