Does anybody agree with me that Piqua vs. Troy is the OLDEST RIVALRY in the state of Ohio?
Depends on what you mean by oldest. If by the first year two rivals played....then no.
This is a list of the oldest HS rivaries in the United States.
http://www.nflhs.com/news/records/11man_team_misc.asp
Oldest Current Rivalries
1875 New London, CT vs.
Norwich Free Academy, CT (143 games)
1882 Wellesley, MA vs.
Needham Heights Needham, MA (117 games)
1887 Boston Latin, MA vs.
Boston English, MA (118 games)
1887 Philadelphia William Penn Charter, PA vs.
Fort Washington Germantown Academy, PA (118 games)
1887 Pottstown The Hill School, PA vs.
Lawrenceville, NJ (101 games)
1889 Baltimore Polytechnic Institute, MD vs.
Baltimore City College, MD (116 games)
1891 Rome Free Academy, NY vs.
Utica T.R. Proctor, NY (112 games)
1892 Abilene, KS vs.
Chapman, KS (83 games)
1892 Pueblo Central, CO vs.
Pueblo Centennial, CO (103 games)
1893 Louisville Male, KY vs.
Louisville duPont Manual, KY (121 games)
1893 Aurora East, IL vs.
Aurora West, IL (112 games)
1893 San Francisco St. Ignatius, CA vs.
San Francisco Sacred Heart, CA (79 games)
1893 Bradford Area, PA vs.
Olean, NY (107 games)
1894 Millville, NJ vs.
Vineland, NJ (136 games)
1894 Canton McKinley, OH vs.
Massillon Washington, OH (113 games)
1894 Marinette, WI vs.
Menominee, MI (98 games)
1895 Tuscola, IL vs.
Arcola, IL (100 games)
1897 Middletown, NY vs.
Port Jervis, NY (126 games)
1897 Ardmore Lower Merion, PA vs.
Radnor, PA (107 games)
1899 Troy, OH vs. Piqua, OH (121 games)
1903 Des Moines North, IA vs.
Des Moines East, IA (102 games)
As you can see, Massillon and Canton first played 5 years before Troy and Piqua.