Do all confessions hinge on these?

Check out this Prayer of Confession from the Episcopal Church Book of Common Prayer.

Most merciful God,
we confess that we have sinned against thee
in thought, word, and deed,
by what we have done,
and by what we have left undone.

We have not loved thee with our whole heart;
we have not loved our neighbors as ourselves.

We are truly sorry and we humbly repent.
For the sake of thy Son Jesus Christ,
have mercy on us and forgive us;
that we may delight in thy will,
and walk in thy ways,
to the glory of thy Name. Amen.

I isolated the sentence in the middle for emphasis. The greatest commandments according to Jesus are to love God and our neighbor. As all other laws and commandments hinge on these, I can wrap up my confession with a single sentence. It makes sense this would be the most important confession of which all others hinge upon.