The EU is already taking Ukraine. Not by force but by politics, we already helped Poroshenko in place there. too bad some countries prefer not to associate with corruption ridden Ukraine [0]. But hey, EU leaders usually don't care what voters think (we got the Treaty of Lisbon after we voted no on the EU constitution).
EU surprisingly did take strong position when Ukraine crisis started. Only way EU countries can stand against Russia is if they have backing of NATO. Without this noone will take the risk.
Because we have a vested interest in keeping peace in Europe. As a country it has worked to our advantage to keep large markets under our protection. Having a dumpster fire in your neighborhood is bad for business.
Extending the zone of safe and free society is definitely in our interests. I don't know when it became in vogue to openly shit on the Democratic Peace Theory, but it's certainly not for a lack of evidence. I guess it's something that you people have committed us to relearning.
But you didn't extend the zone of safe and free society; if anything, you reduced it. And it's not like you can claim it was an unforeseen consequence: Russia told you explicitly that they would "take military and other steps along its borders if ex-Soviet Ukraine and Georgia join NATO" [1], an then they proceeded to do just that in Georgia [2].
So you poked the bear without having any way to contain it, and you shouldn't be surprised that people blame you for it having razed the village.
