Suppose $B$ is some set.
We could change the rules and say that $\emptyset$ is not a subset of $B$. But it would be inconvenient. Here are just two of many examples.
Suppose that $P$ and $Q$ are subsets of $B$. We would like to be able to conclude that $P\cap Q$ is a subset of $B$. This is intuitively appealing, because if every element of $P$ is in $B$, and every element of $Q$ is also in $B$, then surely every element that is in both $P$ and $Q$ is in $B$.
But with your proposal, we cannot say that $P\cap Q$ is a subset of $B$. Because $P\cap Q$ might be empty.
Here is another example. It is tempting to say that $X$ is always a subset of $X\cup Y$. Because surely anything in $X$ is also in $X\cup Y$, which is defined to be the set of things that are in $X$ or that are in $Y$.
But with your proposal, we cannot say this, because $X$ might be empty.
Instead of making a lot of annoying and useless exceptions like those, we find that it's simpler all around to agree that the empty set is a subset of every set.