Same reason Norwegian is considered a separate language for Old Norse (not Old Norwegian). Both evolved over time and are now different from their parent. Due to isolation and a smaller, more homogenous population, Icelandic (and Faroese) has changed less than other Norse languages, but it has still changed.
Because the spelling, phonology and grammar have changed quite significantly, even if an icelandic speaker can with a small amount of effort understand old norse.
Also, because it is a language spoken by icelanders in iceland. As the mainland languages started diverging the need to signifiy the uniqueness of Icelandic became more evident.
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