Hi Fanis,
This is quite debatable in fact. We have taken the decision of making the "Don't assign" the default setting as in a regular project, problems are first split into specific activities and later assigned to resources.
We know this is not the way everybody works though, so we took the following decision: If the filter is set to filter: Assigned to / me, we can assume you are only viewing your own tasks, and if you add a task it is most likely for you and will by default be set to "Me": this applies to all values of the "Assigned to" filter.
Please tell me if this works for you, cheers,
Carlos