Two months is not long enough to expect results to show. I would give it at least six or seven months from the day you began finasteride to see if the treatment appears to be working. Often visible results are not apparent until a whole year after starting treatment. In my case, my hair began thickening very significantly after only about 6 weeks of starting finasteride, but this is not the norm for most users.
In theory, finasteride should "work" for everybody who takes it, in the sense that it reduces DHT in the body of every individual who takes it, on average by about 70%. With less DHT in the body, your hair follicles have more protection from damage caused by this hormone. However, if your hair follicles are very sensitive to DHT, even the small amount of DHT left in the body after taking a dose of finasteride will still cause damage to your hair follicles, in which case you will most likely still experience gradual hair loss despite using finasteride. However, you would lose your hair significantly slower than you would have done if you had never taken finasteride to begin with.
Another point to mention is that there are other factors involved with male-pattern hair loss in addition to DHT. Testosterone, for instance, probably contributes to hair loss to some extent. There is also a second type of DHT that finasteride does not inhibit, which may also play a role in hair loss. There are probably other factors too which are not yet known.
However, in answer to your question, it isn't really possible for finasteride to have "no effect" for any person who uses it, because of the way it works chemically. It might appear to be having no effect, but this would probably be because your hair loss is very aggressive, and even the small amount of DHT still left in the body will still cause significant damage to your hair follicles, and your hair loss will gradually continue. However, you would most certainly lose your hair a lot slower than if you had never taken finasteride to begin with.