And what needs to be first and foremost in anyone's mind is that if you're willing to do what this board wants (The US guarantees their security) then you need to be prepared to go to war with Russia over the Ukraine.

No, you don't. You can have a guarantee that the U.S. will supply them with whatever materiel and resources they need to defend themselves. Smaller countries are frequently able to drive out occupiers and invaders that are much larger than they are as long as they are adequately resourced. We've seen it time and again all around the globe. A force defending their homeland can repel a vastly larger armed force. Heck, that's what we've seen with Ukraine for the last three years - they were perfectly capable of keeping the Russians deadlocked and defending their nation, provided we gave them the resources to do it. These types of proxy wars were more common during the Cold War, when neither the USSR or US wanted to directly engage each other, but still found ways to respond.

That's all you need - you don't need your troops directly engaging the enemy to make it painful for them to invade.

First off, I've noticed that most of (read: 99.9999999999%) of the hostility towards Trump is driven by hypotheticals, such as this one above.

Secondly, Taiwan is of vastly more strategic importance to the US (and the rest of the world) than the Ukraine is. They're not remotely the same situation.

Well, Trump apparently just cut Ukraine off - so clearly he's not all that concerned with making sure Russia pays a price for their invasion.

And Ukraine's strategic importance lies in the global collective security principles that underlie the entire Westphalian system. If you let Russia take a piece out of Ukraine for no reason other than they want it, and they get away with it, then that makes it far more likely that such acquisitions will take place all over the world. Which is the sort of military adventuring that blew up into two full on World Wars, and is vastly more dangerous now that nuclear weapons are in the mix. That was the benefit of the Pax Americana - we ran a massive military and made sure that the world wasn't constantly wracked by military conquest.