So, what, English people are arrogant because the Home Nations play as separate teams in the football, or the Home Nations play as separate teams because English people are arrogant? Again, you're not making much sense.
You mean like football teams? At the world cup there don't seem to be any other provinces/states entered, it's generally all countries in the UN sense of the word isn't it?
No, it isn't. And England is neither a province nor a state, so I reject your wording.
I don't follow football so I'm willing to be corrected here but my impression is Texas doesn't get its own team and neither does a bit of The Netherlands.
Beautiful. The Kingdom of the Netherlands has four constituent countries, all of which compete individually in the football. You don't see Aruba or Curaçao in the World Cup because they're not very good, but they have national teams. French Polynesia, the overseas country of the French Republic, competes internationally as Tahiti. Macau and Hong Kong compete independently from China. Any number of places that aren't independent nation states have national teams: Puerto Rico, Palestine, loads of US and UK dependencies in the Caribbean. Texas isn't relevant.
Why does the UK get special treatment and how is that not a case of interchanging the meaning of the word country?
It doesn't. International football is, in reality, not a competition between teams representing 'countries' but between teams representing national football associations. The Home Nations have individual FAs for historical reasons: the English FA is the world's oldest football association and was formed in 1863, initially covering only London and the south but covering the whole of England from 1877 when it merged its rules with those of the Sheffield Football Association. By that point, Scotland and Wales already had their own FAs. Ireland's formed in 1880. It was nine more years before a non-British FA was formed, by which time the Home Nations were already playing regular international tournaments. Why wouldn't they compete separately?
It's the same in rugby and cricket. You mention the Six Nations: do you know what those six nations are? One of them is Ireland, representing the whole island of Ireland. One of the cricketing 'test nations' is the West Indies, representing fifteen different countries and dependencies. This is why sporting national teams are not particularly helpful or relevant to working out what 'country' means. Try again.