I am the DM, I'm just rather a stickler for rules when it comes to my players' character builds. So, I will have to assume that if even a Druid needs 2 feats to make this work - its going to be grossly out of this player character's capacity in our current rate of advancement in real time.
But what is a sensible "in-world" fluff reason why rangers can't do this mechanically?
They can do this with all vertebrates and a few odd exceptions like the octopus. Animal Companions seemingly become bonded with the ranger's (or Druid's) soul and/or connection to the natural world and become rapidly imbued with additional powers and strengths as a result.
This ranger has specially gone through an apprenticeship with a wizard who has been schooling him in knowledge religion in order to gain a fuller understanding of his goddess's chosen creatures (Apprentice feat). He will next be able to take Vermin Handler, and become able to train and handle animal all vermin like they were "animals", but still can only use non-verminous animals as companions as usual.
Does this imply Lolth reserves the soul-bond between Drow and Spider for only her truest devotees of natural magic (Druids); whose much stronger divine power makes this an option. Rangers on the other hand are unable to truly grasp their own deep soul connection to a vermin in the manner that is instinctive to them with other animals, because they lack the required divine connection to Lolth, and the natural world as it pertains to her? Still seems a little tenuous...