Backing a nuclear armed power into its corner is not a good strategy either.
Unless the aggressor, Russia, is using its nuclear deterrent as a
nuclear threat to bully its neighbors to comply - or else. The nations of the world will not bow and cower into a corner.
Ask yourself, who is sticking their nose into the other nation’s business?
When a neighbor asks for help because a bully and a thief is threatening their family, does one simply ignore them, or does one help them as depicted in the parable of the good Samaritan?
We are fueling a war on the other side of the planet between two neighbors trying to weaken Russia’s national security, —
No, "we" are helping a neighbor in need, and some of its closer neighbors are helping too.
- After
untrained conscripts lost badly in combat last February, the
mothers of the conscripts no longer share Putin's goals for what was supposed to be a short-easy and even "special" military operation. They will not forget the tactical blunder Putin made.
Russia is not arming Mexico against us.
Mexico loves the revenue made in and from the United States. Both of us like fiestas, food, and fun. Russia has no chance of success in this imagined and highly unlikely scenario.
Therefore, We are arguably the aggressor here or at least contributing to any aggression.
Why does this statement feel familiar? Ah yes - the often contested "offensive realism" philosophy of
John Mearsheimer.
We are actively putting missiles and radars into Russias neighborhood, into Russia’s front yard, not the other way around.
Long before the invasion, Ukraine was
not asking for military assistance; so, asking for "missiles or radars" was unwarranted and unnecessary. Issues such as Putin's poisoning of a political opponent in Ukraine provided a lot of suspicion and tension and the military annexation of Crimea didn't help matters.
We are backing Russia into their corner and telling them they have no say in the matter.
Putin could easily say that the (pretend) Nazi's have been defeated and our goals have been achieved. Afterward, withdrawing from the entire region up to including Crimea, and having a big party throughout Russia afterward.
No -corner backing- required.
We deny them their national security concerns.
Yet, Ukraine is not getting acceptance into NATO. It has asked to join the European Union. No threat. Economic opportunity for all.
Reverse the situation and ask yourself, how would we be responding?
I can't imagine Canada or Mexico or even Cuba acting any differently than they are currently acting today.
We would be rattling our nuclear weapons and threatening to blow them up if they come any closer.
Against Cuba, Mexico, or Canada?

I know there is a small probability that all the air molecules can suddenly pack themselves into a small corner of the room you are in now, but that probability is exceedingly small. So small, that it's safe to say that it will never occur under normal circumstances. The same is true with your scenario about "rattling our nuclear weapons" against Cuba, Mexico, or Canada.
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