質問: 住んでいるのが好きです is a fragment of a sentence that is incorrectly constructed - the correct way to say "I like living in [place] would be 住むのが好きです. But why is this? In the present tense, the usual way to say "I live in [place]" is to use the state-of-being 〜ている, e.g., 私は日本に住んでいます。By that logic, "I like living in [place]" should really be "I like the state of living in [place]", or 住んでいるのが好きです. But this sounds weird to me - and the multiple native speakers I've asked have said this is incorrect. Can someone shed some light on the reason? ているのが好き as a construction is definitely not forbidden, as a search on alc.co.jp shows.
回答: Strictly speaking these two sentences have completely different meaning: * 住んでいるのが好き。 - This means that you like the fact someone is living (somewhere). This could be you too, but that's not very clear way to tell it. Let's drop all the wrong usages of this phrase. * 住むのが好き 。 - This means you like to live (somewhere).