Sometimes leaders can still make not rational actions. Putin still didn't need to invade Ukraine. I think the same can happen with Taiwan. For me I also believe "they don't really need Taiwan" but I think a lot of Chinese people think about it not in economical reason but national/historical and military reason - many of them say that china is really afraid if US will start putting their own military bases in Taiwan so they supposed to don't care much about Taiwan as more wanna control the land.
Don't really want to defend Putin, but consider that Russia would at the very least lose the naval base in Crimea, if the Ukraine entered NATO. Also, in 2013, the EU put an ultimatum to Ukraine to choose between the free trade with EU or free trade with Russia.
Perhaps Putin's action isn't as irrational as it seems?
Russia losing free trade with Ukraine is pretty much nothing compared to the economic damage caused by the sanctions, and loss in gas sales to the EU.
Putin's action would have been rational if he had captured Kyiv in a couple of days or weeks, and managed to install a puppet government. IMO the whole thing was based on bad intel, lies, corruption and yes-men who told their superiors what they want to hear, rather than what was the truth about Ukraine's defense capabilities. After that Putin couldn't back off without losing his face, and obviously loss of human lives and economic damage mean nothing compared to that to him.
