The case against:
Their language is a Finno-ugric language like Hungarian, where all the other Scandinavian languages are Indo-european. In fact they are all derived from Old Norse which is an old Germanic language which has its closest descendent in the form of Icelandic.
By looking at the map you can see that Finland is not part of the Scandinavian Peninsula, neither is Denmark, but it forms a peninsula jutting into the heart of scandinavia. Iceland is also not in Scandinavia, but there is documentation of the settlement of Iceland by vikings, so their claim is not questioned. Finland on the other hand is really more like a northwestern extension of Eurasia.
The Case for:
Finland is predominantly Lutheran (90%) and has a population of 6% ethnic Swedes which reflects the long occupation of Finland by Sweden from the 1150's to 1809. King Erik Christianized them. Since this occupation began before "civilization" had even gotten off the ground, it would not be an overstatement to say that Finnish culture was in good part scandinavian.
http://virtual.finland.fi/finfo/english/chrohist.htmlWithout claiming some kind of orientation towards scandinavia, Russification would have more likely occured during the period from 1809-1918. By identifying themselves as scandinavians they could gravitate to something other than being an isolated nation occupied by Russia.
Finns are hard to distinguish from other scandinavians until they speak.
So there you have it.