Many of us grew up hearing a list of writing rules: don't begin a sentence with a conjunction; never use the first-person "I"; don't end a sentence with a preposition. Some of the rules we've learned have fallen out of fashion, but others seem to endure.
When Professor Anne Curzan teaches writing courses, she always asks her students which rules they heard growing up. Over the years, she's been hearing from more and more students who were taught not to use adverbs. Not to use adverbs sparingly, but to never use them.
While we agree you should be careful with adverbs, abolishing them completely may be too simple.
Adverbs do a lot of work in English. They can modify verbs, as in, "The robot walked clumsily to the door." They can modify adjectives, so you can say things like, "The movie was surprisingly funny." They can modify other adverbs, and they can even modify entire sentences. Their flexibility makes them one of the harder parts of speech to neatly categorize.
In his book "On Writing: A Memoir of the Craft," author Stephen King advises writers to use adverbs sparingly. His reasoning is that a stronger verb can often accomplish more. Instead of saying someone "closed the door firmly," a writer might say the person "slammed the door." Rather than writing that thunder was "very loud," a writer could describe it as "deafening."
Words such as "very," "quite," "rather," and "somewhat" can certainly weaken a sentence when a more precise word would be stronger. Still, not every adverb is a sign of weak writing. Some add information that would otherwise disappear. For example, if someone shouts, they can do it excitedly, urgently, or menacingly, and each adverb changes the meaning in a way that a stronger verb alone may not capture.