Streets will only be treated as oneway in your network dataset if you have created a restriction attribute which constrains them to be oneway. Please look at your analysis layer's property pages and see which restriction attributes you have turned on. Then, simply turn off any oneway restrictions or other restrictions which you did not explicitly mean to use.
Note that, when you are building your network dataset, the build process may automatically recognize certain fields in your source feature classes (e.g., a field named "Oneway") and create attributes based on these fields. This is only done for common attributes used in transportation analysis (such as oneway restrictions), and it may explain how you ended up with such restrictions in the first place. However, you can always simply remove them during the build process, if you like.