Courts serve all types of purposes and each type of conflict is resolved by a different system of justice depending on who the parties are and with whom they have grievance. Very roughly you can consider :
- Citizen vs Government → Criminal Justice System
- Violations of Criminal Law
- Government vs Government → Impeachment
- Violations of Constitutional Law
- Military vs Military → Court Martial
- Violations of the Uniform Code of Military Justice
- Citizen vs Citizen → Civil Justice System
- Violations of Common Law
This isn't to say that constitutional law is limited to matters of impeachment, but where constitutional law acts against an individual agent of government the litigation process happens under the umbrella of impeachment.
A private citizen is only subject to criminal and common law. Just like a private citizen cannot be brought before a military court martial, so neither can they be impeached, for both of those are violations of a set of rules that private citizens have not elected to subject themselves to. Those rules only apply when an individual takes up formal service to the bodies where those rules apply.