I don't usually interfere in queries about regular soldiers, as my specialty is the irregular ones, but I wanted to add information about Ben Beaty's military service record from the online Missouri State Archives access via the MO Sec'y of State's website at http://www.sos.mo.gov/archives/soldiers since in this case it has so much to add.
These records state:
Private Ben Beaty and Private L. P. Beaty were both members of Company F, 16th Missouri Infantry Regiment (CSA). Ben was paroled at Shreveport, LA June 1865. Both Ben and L. P. attented the 8th annual reunion of "Ex-Confederate Missourians Association" at Nevada, Vernon County, MO in 1890. As of 1890 Ben was a resident of Petersburg and L. P. was a resident of Huntingdale. L. P. also attended the Sixth Annual REunion of Missouri U. C. V., the Norval Spangler Camp # 678 at Clinton, MO July 1902, according to Missouri Historical Society records.
Also, these records also state about Ben that:
date of birth: April 26, 1839;
place of death Clinton, Missouri;
date of death: August 12 1908;
father's name: Joseph Beaty;
mother's name: Mary Beaty;
maiden name of wife: Louisa Kimsey;
date and place of birth: January 16 1841, Clinton, MO;
date of death: Sept 4 1898;
her father's name: James Kimsey;
her mother's name: Susan Kimsey.
It was partly because this source revealed so much information that I brought this forward. As to your initial question as to why Ben was called "Captain," I have no idea. I wonder if this was a title given to him post-war for some reason. Local Henry County records may reveal this.