Why do people speak icelandic?

Answer 1

Danish is a mandatory subject in the schools of Iceland, because:

Iceland was under the control of the Danish Crown from 1380 to 1944.
Also note that Iceland was a Norwegian possession from 1262 to 1814, but Iceland along with Norway was ruled by Danish monarchs from 1380.

In the early 1800s, Denmark was involved in the Napoleonic Wars, lost by some measures in war of some sort with Sweden, and Norway (which had been part of Denmark since 1536) was ceded to Sweden, but Norway's overseas possessions (including Iceland) remained under Danish control.

-I also noticed that you asked "why do some Icelanders speak Danish?"

Most, if not all Icelanders that aren't halfwits can read and write Danish quite well, but speaking or understanding spoken Danish is completely different.

The, uhm "old ppl" of Iceland you might expect to speak excellent Danish, and rather dreadful English, though many "old ppl" adjusted well with post-war British influence and speak very good English...

Answer 2

For the same reason as people speak any language: they were born speaking it. Icelandic is derived from Old Norse, which used to be spoken across Scandinavia and is related now to Swedish, Danish, Norwegian, Faroese, etc.