To the "global war on terrorism" simpletons in Washington, it's ABC to classify as terrorists people or groups that actually want to defend their own constituents, or country against the USA's demands that they go along with whatever the US government, Israel and their associated corporate interests want to do in their territory.
What's the matter with the EU? Don't they know that Hezbollah is the devil?
One thing that can be said for the EU is maybe they think it's a good idea to sit down and talk with people you have big differences with, rather than pout and bully (bu they haven't seemed to figure this out regarding Iran and the nuclear issue).
Another factor is that the EU correctly sees Hezbollah not as some international terrorist organization, but as a major political party in Lebanon that you have to deal with.
Contrary to howls from the professional ignoramuses in the House and Senate and the lobbies that pay them off, Hezbollah isn't an arm of Iran. It came into being in 1982 as an alliance of Shiite militias that were formed to defend their country from an invasion by a foreign power...Israel. The Shiites populate Lebanon's southern border with Israel; they also comprise 43% of the population.
Israel's excuse for invading Lebanon in 1982 was to find and destroy the PLO leadership based there. The PLO, Arafat and his fighters ended up moving to Tunisia. Meanwhile, not wanting to waste their whole invasion, Israel proceeded to lay waste to Beirut and other cities in Lebanon, killing around 15,000 people and allowing their allied Lebanese militia to massacre hundreds of unarmed Palestinian refugees.
After declaring their attack a great success, the Israel army withdrew; but stayed to occupy the south of Lebanon, in practice extending the Israeli border 20 miles northward. It was in the Shiite villages that the organization that became Hezbollah began to come together. Hezbollah carried out a successful guerrilla war and Israel was forced to withdraw completely from Lebanon after 20 years of struggle. The great majority of Lebanese celebrated Hezbollah's driving out of the IDF from their country. Hezbollah became a much stronger force that that of the official Lebanese army, which was small, ineffective and paralyzed by the faction ridden politics of Lebanon.
Following it's independence from French colonial rule, Lebanon was left a legacy of demographic/tribal politics. The government was set up to balance between organized blocs of Maronite Christian, Sunni and Shiite Muslim and Druze (a different type of Muslim community).
Israel and the US favored the dominance of the Maronite Christians, who were more pro-West and ran from conservative to reactionary (the main Maronite group calls itself the Falange...if you think that sounds sort of well...fascist, you're right). In 1982 Israel set up a a Maronite army to operate in the south of the country during it's occupation. This army didn't survive the IDF withdrawal.
The successful struggle of the Shiites against the Israeli army and the emergence of Hezbollah as a major player in Lebanese politics did not make the US and Israel very happy. Israel invaded Lebanon a second time in 2006, claiming that an incident on the border (which was similar to other incidents that happened over the years) justified a full scale military attack. Israel also said that Hezbollah had acquired too many tactical rockets near the border and that the IDF needed to find and destroy them.
That invasion was a flop. Hezbollah blunted the Israeli thrust and forced the IDF to withdraw. Again, Israel didn't want to let their invasion go to waste, so their air force ranged up and down Lebanon bombing roads, bridges, factories, anything they thought might be useful for a nation to function. About 2000 people were killed. None of them had anything to do with the fighting at the border.
Since the 2006 invasion Hezbollah has grown to be even more prominent in Lebanon, taking on a fairly large role in a coalition government. Maybe you can see why most Lebanese and the EU don't agree with the Obama administration's shrill terrorist bating of Hezbollah.