Do I HAVE to put sugar in this pickling recipe?

You could use honey instead. I always have pint jars of pickled onions (a blend of red and yellow), of small mushrooms, of whatever strikes me as interesting to pickle. For each jar, the solution I use is comprised of: 4 ounces white or rice vinegar, 4 ounces apple cider vinegar, 3/4 teaspoon sea salt, and 3/4 teaspoon sugar. To substitute honey, simply use half as much of the sugar measurement, as honey contains twice the sweetness of sugar. As Emma writes, it is important to add some element of sweetening in order to balance the vinegar and salt. I pack my jar(s) full, and bring to a boil the vinegars, salt, and sugar or honey, then pour the jar full.

I also drop into the bottom of my jars an assortment of whatever I have on hand: a couple of garlic cloves sliced, a dry red chili (I like Japones), a few peppercorns, a bay leaf or two, some toasted mustard seeds, though not all at once, you understand.

Hi! This is a vinegar-based, fridge-stored pickle—so it's pretty open to adaptation. That said, sugar is a standard ingredient in vinegar brines for flavor. Without the sugar, the pickles will turn out overly sharp and unbalanced, so I wouldn't recommend skipping it.