I put on a glove in my shop yesterday and, next thing I knew, this guy was running up my arm :
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There are misconceptions about brown recluse spiders. Everyone has images of horrible skin reactions from bites but, brown recluse spiders are not aggressive. In fact, they're very shy ; they'd be much more likely to run away than to bite. Also, if one is bitten, it's not a sure thing they will have a bad skin reaction. Many people are bitten and barely know it.
There is, however, a clear danger. The brown recluse is one of the most venomous spiders in North America and can cause a really bad reaction, while rarely death.
My attitude is to be aware but not have an inordinate fear of these spiders.