I have feelings about the term "bug," and to me, it's association with hemipterans always seemed quite forced and arbitrary. It's a much older word in English than "insect" or "arthropod," which of course, are Latin words, and without it we don't have a good term for this category of animal. (as many would argue "bug" covers only insects, arachnids, centipedes and millipedes, and not crustaceans, rendering it not entirely synonymous with "arthropod")
In addition to this, be happy that there are only two kinds of dangerous spiders in the entirety of the US: brown recluses and black widows, neither of which are particularly aggressive spiders (in fact, it's been demonstrated that brown recluses only bite when pressed into your skin by something else, like say, a pair of pants in which they were hiding before you put them on). The only kinds of spiders I will kill in my home are these two - the others either get left where they are or placed outside (generally I will remove big wolf spiders and place them outside.)
But yes, I agree. Many of us are far too fearful and/or unfair to spiders (most arthropods, frankly).
I agree that the term "bug" as technically applied to hemipterans is kind of silly and forced. I tend to use the term "bug" even broader than just arthropods (though largely arthropods) but also to include things like worms and snails and slugs, pretty much anything that is small and can be found in the garden and woods and sometimes in your house. I'll even occasionally apply it to some crustaceans, namely shrimp, because it is fun to describe consuming them as eating "sea bugs." I guess "bug" is kind of like "vegetable" and "tree" in that these words do not have technical biological meanings, but are used widely in common language and serve as a broad descriptor for a variety of things that we all know to fit in the category.