Why can't some stative verbs be used in the passive? We can't, for example, passivize resemble, but we can passivize know, love and like?
Syntactically transitive verbs that don't permit a passive are typically either stative verbs (have (own), lack, deserve, suit, fit, weigh, cost, etc), symmetric verbs (marry, meet) or both (resemble, equal).
That symmetric verbs can't be made passive is probably because the main point of using a passive is to alter the asymmetry of a construction by promoting the object; when the construction is symmetric this doesn't make any sense.
Meanwhile, the lack of activity in stative verbs makes elevating the object to a subject a bit strange (though not impossible). That some asymmetric stative verbs do allow it, while others don't, is probably mostly chance enforced by usage. Verbs that don't permit passives sometimes function more like copulas than regular transitive verbs, linking the subject with a property rather than linking two participants (eg weigh, cost). Still, I doubt there is a good reason why "I am fitted/suited (by this hat)" is ungrammatical, while "This is known (by me)" is fine.