If the same committee writes the rules, accuses people of breaking them, and decides their appeals, a complaint against the committee has nowhere independent to go. Separation of powers breaks up that concentration. Different bodies perform different governing functions, with procedures connecting and constraining them.
The familiar US constitutional example separates legislative, executive, and judicial functions while also creating checks between them. Separation does not mean complete isolation: institutions must still cooperate, and some decisions deliberately require more than one body's involvement.
Independence has to be real
An association could adapt the principle by letting members adopt rules, an executive apply them, and an independent panel hear disciplinary appeals. This gives a member challenging an executive decision someone else to hear the complaint.
The panel will not be meaningfully independent if the executive can dismiss its members whenever they disagree or controls all the information they receive. Appointment, funding, access to records, and protection from retaliation influence whether a formal division becomes an actual constraint.
Dividing power can also create deadlock and responsibility gaps. Each body may blame another for inaction. The design therefore needs ways to resolve conflicts without simply restoring unchecked control to one actor. The point is to make certain abuses harder, even when that makes some legitimate actions less convenient.