I don’t know about breaking spaghetti, but putting them in a too small pot can ruin them. As my mother always used to say, “let the pasta swim! They must swim in the water!!” (Imagine in a strong Italian accent).

If you don’t have enough water the pasta doesn’t release enough starch (or something like that) and gets a bad flavor and texture, not mention not mixing well with a lot of sauces. Always use a bigger pot than you think you need with Italian food.

Edit: I was once at a German relative’s, and I kid you not, she had no pot of any kind. Nothing. So I ended up making spaghetti in a Teflon pan. Did not taste good.