Question

What was a reason that northern leaders disagreed over the south rejoining the union

Answer 1

Various ideas of reconstructing plan.  The radicals vs. ten percent plan.  
Radicals wanted southerns to be punished more harshly.  
Radicals also wanted freedmen to be given full rights.  Full voting.  (No Jim Crow laws.)  
Ten percent plan.  Was a bit softer.  Only ten percent swear an oath, state can be reunited.  Sometime called the Lincoln plan.   

(Just think what would have happened if the Radicals would have taken over.  AND stayed for several decades as part of the reconstruction plan.  There would have been no poll tax, literacy test, grandfather clause.  So much hatred today...   Probably not.  No freedom rides, marches, or sit - ins in the 1960's.  Just a thinking a speculation idea...)