If the people of Ukraine want to get in NATO for protection, how is this the West being arrogant?
Study the outrage in the USA when Russia put nuclear missiles in Cuba, when Cuba, a sovereign country asked for those missiles (aka The Cuban Missile Crisis). Substitute Cuba for Ukraine and USA for Russia and you will be begin to understand the Russian point of view. But hey the West is Right, We are the Good Guys, always on the side of Freedom and Democracy so we can't be wrong. Just ask the Palestinians in Gaza.
You haven't considered the consequences of folding to nuclear blackmail. That increases the chances bad actors will use nuclear blackmail again (because you've shown it works), and it increases nuclear proliferation because small states start feeling unsafe if larger states refuse to help them defend themselves out of fear.