When the impostor posing as Matthew Ordway knocks a terrarium of black widow spiders onto the floor and Watson reaches for the gun among them, Holmes shouts "Stop it, Watson! Those insects are deadly!" Spiders are not insects, and Holmes, having just revealed Ordway to be an impostor on the basis of the man's lack of knowledge about spiders, should know this.
The first time Sherlock Holmes refers to the deadly spider that caused all of the suicides and nearly killed him, he calls it an "insect". Spider are "arachnids", which have 8-legs and 2 body segments, unlike "insects" which are 6-legged and have 3 body segments. Holmes is unlikely to make such a mistake.
Adam Gilflower is summoned by Holmes to identify the dead spider because, says Holmes, "I believe you know more about spiders than any man in London." Gilflower identifies the spider, but incorrectly observes that it is "the deadliest insect known to science."