Irgun and Haganah
The definition of terrorism is wide and differs from one place to another but if we go by what this French Revolution leader, Maximilien Robespierre, proclaimed in 1794, "Terror is nothing other than justice, prompt, severe, inflexible; it is therefore an emanation of virtue; it is not so much a special principle as it is a consequence of the general principle of democracy applied to our country's most urgent needs."(Wikipedia, definition of terrorism.) Then we can say that these two organizations or to be more specific the Haganah was a terrorist organization.
Since the very beginning the main idea or purpose of the Irgun was to boycott the British who really opposed the idea of a Jewish State in Palestine soil, one of the measures to prevent it was the reduction on the immigration quotas, which really helped to grow the resentments against Britain. WW II began but the idea was still there and everything was getting ready for the aftermath of the war. The Nazis were killing the Jewish all over Europe so the Jewish decided to help the British by joining their ranks in the military.
On the other hand the irregular military factions (the Irgun and Haganah) started to attack Arabs and British personnel in 1944. They thought it was time to take justice into their own hands because they were not going to wait for the British to allow them to create the Jewish State. An event that stirred things more was the assassination of British minister of the state for the Middle East, Lord Moyne, it was carried by the Lehi the other armed group. So, we can see that the tactics used to achieve their goal was what we can consider "terrorism."
A series of events made the situation more unstable; the Haganah started attacking Britain communications in Palestine, the Irgun continuous actions like the partial destruction of the King David Hotel in Jerusalem, and the US opinion about the British capability to control this situation, later led to the...