You must not, my lord, mistake my niece. There is
a kind of merry war betwixt Signior Benedick and her. They never meet but there's a skirmish of wit between them.
This is Leonato, in the very first scene, teasing Beatrice but also explaining to the messenger that his niece and Signor Benedick always have this sort of "merry war": they're always swapping insults, and causing trouble with and for each other. It's an interesting one, because, like the play itself, it's half-bitterly serious and half-comic: it can be quite difficult to tell which.
Here's Antonio and Leonato teasing Beatrice at the party scene, Act 2, Scene 1, and teasing her along the theme which she is most usually teased about:
By my troth, niece, thou wilt never get thee a husband if thou be so shrewd of thy tongue.
In faith, she's too curst.
Beatrice is older than Hero (sometimes, even, played as being middle-aged!) and remains unmarried. Leonato and Antonio wind her up for being too "curst" - quick-tempered and quick to insult - and tell her that she'll never get a husband. It's a joke, but it also has a serious side: Beatrice really is quite vulnerable and upset about the fact that she doesn't have a husband - and equally touchy about the relationship she has previously had (clued at by the text, but never explicitly explained) with Benedick. It's tears behind the smile sort of thing.
But the answer to your question - she's teased because she is unmarried.