Will used to mean want (and sometimes still does) but in other Germanic languages, such as Dutch and Norwegian, the cognate still means want.
What was different about English to cause this?
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Linguistics is an old field, its almost as old as writing itself. The first writing systems weren't very precise. Any syllable that sounded similar was represented with the same symbol. Some however did notice the different syllables that one grapheme could represent, and thus began research that evolved into phonology. However, this remained the only field of linguistics up until modern times. You'll notice that its the most developed field of linguistics. Its well understood how the phoneme inventories of languages and the pronunciation of words change over time, but virtually nothing is known of how grammar changes. The only thing that's really known well is the evolution of case endings, which is solely because it overlaps heavily with sound change.
As for jlawler's comment, that doesn't mean its impossible to determine. We do have information on how a word's meaning can change over time. And we do have information on the evolution of past tenses in the Germanic languages. Several times German's imperfect and perfective have merged, only for another perfective to develope and to later merge again.
To me, how 'will' came to be a future tense marker is pretty obvious. People probably improvised a future tense by saying 'X wants to Y'. This later became a grammatical particle. The question is more how the modern word 'want' developed. Looking up its etymology, it originally meant 'to lack'. It would appear that over time, English speakers came to associate 'lacking something' with wanting it. I imagine this was strengthened as 'to will' lost its original meaning. This is also evident in the noun 'want', which started off meaning 'deficiency', but later came to mean 'something not possessed but wanted'.
Interesting side note, 'ich will' still means 'I want' (the infinitive form is 'wollen', but the o becomes an i in several conjugations). They instead use their verb 'werden' meaning 'to become' to form a future tense. Though it does still maintain is independent meaning of 'to become'.