The Wikipedia article says it prevents conversion of testosterone into dihydrotestosterone by the enzyme 5α-reductase, and also affects the GABA system. Particularly relevant quote: "Reduction of GABA-A receptor activation by these neurosteroids has been implicated in depression, anxiety, and sexual dysfunction." More specific than that is way beyond my understanding of these things.
Like I said, any more is beyond my level of understanding of these things. All I can say for sure is that the GABA system is incredibly important, and kinda delicate.
Read up on delirium tremens, for example: long-term alcoholics, and benzodiazepine and barbiturate addicts need to be really careful in stopping their use of those drugs — they could die if they aren't. Those drugs also affect the GABA system.
Maybe the long-term down-regulation of some aspect of GABA-A metabolism by finasteride's preventing the formation of an agonist for those receptors becomes permanent or semi-permanent after a while? I really don't know.
https://en.wikipedia.org/wiki/Finasteride#Mechanism_of_actio...