I have no idea who you are quoting. But bowing down to nuclear threats
increases the chance of nuclear war. This is because it will cause more nuclear threats in the future, and also
strongly incentivize most non-nuclear countries to acquire nuclear weapons.
We currently see NATO provide very stern back-channel warnings against nuclear weapon use to Russia. This is deterrence, which again decreases the chance of nuclear weapon use.
Similarly, providing military support to countries that are invaded decreases the risk of future invasions all over the world, since it makes the cost that much higher for someone who wants to achieve their goals by military force.
We can all agree that the Iraq war was a terrible mistake, and that the United States has made many such mistakes. But the current support for Ukraine's self defense is a completely different sort of situation, and has little to do with allegiance to any particular country.
It does also support the USA's geopolitical interests as a side effect, which is why the US is so strongly involved, but the deterrence effect is the main reason it's important. It serves the same goal you're aiming towards -- long-term peace and trade, and ensuring nuclear weapons are never used.