I don't think that's paradoxical at all.

This is right in the EU's backyard. If it were to heat up they'd actually have to deal with things like refugees and the possibility of war spreading to their members. They probably also want to be very explicit about their (lack of) obligations in this case, I mean people are already acting as if this calls into question how steadfast they'll be in defense of eastern EU members.

We have two options. First, Putin is bluffing. This is what most people believe (and hope). In this case giving Ukraine more weapons won't hurt anyone. Option two is that he is really planning some offensive action this winter. In this case sending weapons to Ukraine could help in slowing the Russians down. It could also help in decimating their army - if they unmask as a ruthless aggressor, it is in the interest of the whole civilization, not just the EU, to limit their impact.

There are countless options.

Another option is that both the EU and Putin know Russia does not have the conventional strength to attack the EU, but does have the manpower to attack other unaligned countries. And so, the EU has decided to prioritize their other interests over standing up to Russia.

It's just our way of flipping the bird to Victoria Nuland for saying 'Fuck the EU!'

But don't take it too seriosly, that was long ago, now our brand new and most competent foreign affairs sock-puppet goes with the flow.

What does "the rest of the EU" mean here? It's not like the USA are a member.

That doesn't seem paradoxical at all, the US is the strongest global military power and the EU lives under its defense umbrella anyways