Well, it sounds kinda weird if you think about it. But it comes from "ssać" (to suck), because mammals suck their mom's milk... (can you say that in English? - well, anyway, you know what I mean).
If you really want to know why: this word comes from Old Slavic sъsati, it ended up with a double letter due to the loss of the weak vowel ъ (it was pronounced like the "u" in "pull")