"manifest their resolve to repudiate" doesn't necessarily = "make a profession of faith".
It's not EXACTLY the same thing, but in practice, it is. It's two sides of the same coin. If you "repudiate errors" of V2, this means you are "abjuring errors" of your past life, which is an indirect way of professing your faith in Tradition/Orthodoxy.
V2 teaches the faith, but it's a corrupt faith. So if the priest instructs the person on which parts of the Faith are corrupted, and they learn the Truth, then by "repudiating" the corruption, you are, in effect, professing your faith in the non-corruptible Truth.
Most V2 catholics (of good will) are material heretics, which means they *think/want* to profess the Faith. They'll readily agree with saying the Creed, the Catechism, etc. "Professing the Faith" is not the problem; getting rid of their corrupt understanding of certain doctrines, is the problem.
So if they repudiate their errors, they are correcting their personal faith in the Church, which was always there (just defective).