When making batter/dough, why is it really bad to clean your spoon by hitting it on the edge of the bowl a few times?

Oh, those cooking myths!

Whenever you think you have heard them all, there's a new one. In a yeasted dough, the yeast is perfectly fine with being tossed, beaten and generally mangled. The little yeast cells couldn't care less about what you do in the initial stage of mixing and kneading. (That's obviously different when you consider the dough after the bulk raise: You want to keep the existing bubbles, sometimes more - think baguette or ciabatta - sometimes less, when you punch out the larger ones for a smoother texture, but I digress.)

What is an issue, is the kind of air that didn't come from yeast digestion and is safely entrapped in a gluten network, but the air that was beaten into the batter mechanically. In the oliebollen recipe I have, you make a fairly liquid yeasted batter and finally add beaten egg whites. Now, thats a material that doesn't take well to being jostled around. Just consider how carefully the egg whites are usually incorporated: There's even a cooking term for the method, you fold them in, instead of stirring like crazy.

Many bakers will handle a batter with incorporated egg whites very carefully, because they don't want to burst those precious bubbles¹. But unless I am working with something super delicate, a gentle tap of the filled pan can help too-large bubbles rise to the top (and subsequently be pierced) instead of creating unsightly cavities or worse, darkened patches on the surface.

The kitchen rule of "don't bang the spoon on the bowl" may well originate from there - but then the rule applies to all kinds of batter with stiff egg whites. You can be on the very safe side and desist, but I am quite sure that it won't really matter if you tap gently. On the other hand, wiping the spoon with your finger or a spatula means you get all batter in your bowl, and not in the sink, which the frugal me appreciates.

Not tapping the spoon will also prevent chipping the mixing bowl, which in the past was often made of clay or ceramics, and avoid splattering.

¹ That's something that fires back in macaron making, where you have to purposefully destroy some of the bubbles...

There may be a few batters that are sensitive to shocks or loud noises, but most will not be (see Stephie's answer for more detail).

In my household, the real reason for not beating the spoon was always clearly about protecting the dishes, not the food. Mixing bowls can chip, crack, or dent (depending on the material). If the bowl has a lid, then damage to the lip of the bowl can prevent the lid from fitting. If the bowl is ceramic or plastic, an impact may crack the bowl, which may even get shards of bowl material in the batter.

For cooks that like their cookware to last (my mother's pots and pans are older than I am), banging a spoon on the bowl is unthinkable. You either scrape the batter of with another spoon, or you flick the spoon into the bowl without making contact (the motion is similar to the one used for banging the spoon on the bowl).

Another reason not named so far, that applies even to combinations of spoon and bowl/pot that are mechanically perfectly fine with hitting and vibration-insensitive contents:

Not banging safes the nerves of everyone else in the house.

Keep in mind that sound transmitted through solids travels surprisingly well and table or sink can act as sound board... So, extra points if the kitchen table touches the radiator or some pipe or if the bowl/pot is in the sink (= mechanically connected to the water piping).