What roles of the president could be at odds with one of their other roles

The two roles that could be at odds with one another could be Party Chief and Chief Executive

That is because he might introduce laws or executive orders that are only there to protect their party which could be a conflict of interest. This was historically seen in the spoils system where the president would give positions of power to party members just by their virtue of being party members.

The  pan-african movement  was an "emotional, cultural, psychological and ideological  movement  that began among the  african  dispora in the western hemisphere, for a closer  purpose, so that  african  people could feel secure, attain political, economic as well as psychological power visa vis other races or world regions" .