For quite some time, Ukrainian nationalists have been actively putting forth opposition to Ukraine joining the EU and NATO. These efforts became much stronger in the summer and fall of 2013, when then anti-Ukrainian dictator Viktor Yanukoyvch was very pro-EU and doing everything to join it (it's worth mentioning that Yankovych was one of the first officials in Ukraine to officialy start legalizing LGBT).
When Yanukovych ended politics of trying to join the EU and decided to get closer to imperialist Moscow, mass protests started in Ukraine. Nationalists joined these protests, but did not support the slogans regarding the need to join the EU. Quite telling, in this sense, is the appeal of the Tryzub movement (the movement that ended up founding and being the main part of Right Sector) from November 20th 2013. In this appeal, Tryzub clearly stated: "We, Ukrainian nationalists, support the idea of working economically with countries in Europe and signing agreements for this, if these agreements don't conflict our national interests. However, limiting ourselves to only a bit and not aiming for all that belongs to us means preparing ourselves for strategic failure. At the same time, we feel that the Eurohisteria now present in Ukraine is irrelevent and, above all, distracts Ukrainians from the main thing: there is no alternative other than a national revolution. We are AGAINST Ukraine joining the EU, because we understand well that the only thing European in the EU is the name. Antichristianity, liberal totalitarianism, multiculturalismn pseudotolerance, destroying the very roots of European peoples, artifically replacing Europeans with emigrants from Asia and Africa, the promotion of satanism and types of satanism: atheism, homosexual dictatorship, consumerism and so forth - at the very base of these we see how true national and human ideals, including Ukrainian nationalism, are different from this new form of pseudoeuropean imperialism. We must say, unfortuantely, that the modern EU is a new type of imperialist creation, whose main function is destroying nations - and thus is a threat to the very existance of the Ukrainian nation".
It's worth remembering, that during January and February 2014 many Ukrainians became dissapointed in the EU and NATO because they did nothing to remove the Yanukovych oligarch regime in terms of sanctions and etc (in reality, the west did not want to remove his regime, but merely change the geopolitical orientation of the regime). However, when Russia started armed aggression in Crimea, Ukrainians again started look towards the west, started talking about joining the EU and NATO. Yet,the cowardice politics of the west towards Russia is dissapointing Ukrainians and showing them, that we can only rely on ourselves. This creates a perfect atmosphere for promoting nationalist ideas.