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.
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.
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