The group was against Nazis for many reasons. The Nazis had tried/attempted to either put all of the Jews in a concentration camp or to kill them all. They had caused the Jews a lot of problems and for them to go into hiding.
The group faced many hardships such as sickness. Sicknesses throughout the Annex has caused many deaths and depression.
Anne and Dussel didn't argue frequent but when they did, it was over the table. They each felt that they deserved the table time and wouldn't argue a lot over who had gotten to use it.