Taiwan is literally an independent country, although they promote a policy of strategic vagueness about this in hopes that it will discourage China from launching an invasion. The arguments China makes for its ownership of Taiwan are no more defensible, and arguably less, than Portugal's justifications for maintaining ownership of Goa.
It's not a country according to the UN because China is a permanent member of the UN Security Council.
Does Taiwan have its own military? Yes.
Does it issue its own passports? Yes.
Do you have to have their visa to land there? Yes.
That's a country.
And you, sir, on this thread, sound more like a propagandist than someone trying to have an actual conversation. You're not here to converse, to listen, but only to trumpet your talking points. That's not what HN is for, and you've been here long enough to know it.