Finland has many similarities in culture with it's other nordic neighbors, however it is not considered to be apart of Scandinavia. Finland was under the rule of the Swedish empire for many years and there are parts of Finland that people primarily speak Swedish. Even the northern part is technically located on the Scandinavian peninsula. So why isn't Finland considered to be Scandinavian?
There are a variety of factors involved in answering this question and I will have a shot:
Language: It is true that Finn-Swedish is a large minority language in Finland it is still estimated to be mother tongue for roughly 5% of the population (though it's forced on the rest in high school) those mainly in the west on The åland islands(a whole other debate) Finland proper (the original 12th century power base of the Kingdom of Sweden) and the border region around the Torne valley. Despite this the rest of the nation speak a language that is utterly unrelated to any of the "Scandinavian" languages. It is Finno-Ugric as opposed to Indo-European so it isn't even as linked as say Swedish is to Portugese let alone being nearly mutually intelligible like most Scandinavian languages.
Geography: Besides the Bothnian gulf splitting the two countries all the way up to Lappland there is also a giant river (The Torne) that denotes the Finnish border and acts as a natural barrier between peninsula and mainland.
National identity: During the Finnish war the Swedish Kingdom lost control of what would become the Grand Duchy of Finland (and later give or take Finland) to the Russians who moved the capital to Helsinki in 1812 (it was up to this point a back water with a lot of potential and a nice fort) away from Turku in the southwest; this allowed a greater percentage of the population of the capital to be Finnish. It seems small but I feel it was a big deal
Then in the mid 19th century you have a cadre of (swedish speaking) academics chief amongst them Johannes Snellman who start to push the Fennisation of the country by publishing the first Finnish language newspaper and calling for other academics to work, think and publish in what until then was seen as the language of peasants. (I really like the (ironically originally in Swedish) poem from this era: Swedes we are no more,Russians we cannot become, therefore Finns we must be).
This movement gained momentum with the translation of the Finnsvensk story "Tales of Ensign Stål" into Finnish, the dissemination of compiled Finnish folk tales "Kalevala" in Finnish along with a growing Finnish speaking literati class.
This later led to independence and a Finnish sovereign state but the importance re: your question is that by the late 19th and early 20th Centuries Finland thought itself as a land apart from the Scandinavians in culture.
Citations: Demographics: http://www.stat.fi/til/perh/2014/02/perh_2014_02_2015-11-27_tau_004_en.html Helsinki: http://www.helsinki200.fi/en/helsinki-1812-2012/1812-emperor-alexander-i-promotes-helsinki-capital-grand-duchy/ Snellman and the Fennoman movement: http://www.suomalaisuudenliitto.fi/?page_id=33 http://www.suomalaisuudenliitto.fi/?page_id=33