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So?  Faith is a necessary cause of justification.  This does not mean that the Sacrament is not.  In fact, Trent teaches that the Sacrament is necessary for justification also.  So what's your point?

It sounds like you're trying to turn a necessary cause into a sufficient cause, and that's faulty logic.

I cannot live without water.  From which you conclude that I can live on water alone.

Hold on there. I know some theologians teach that - maybe even St. Thomas - but it contradicts Romans, Galatians, Hebrews (regarding the old sacrifices which didn't justify from sin), and the Magisterium of the Church. I'll find the quote from Denzinger, but I'm pretty sure that one of the popes quoted in there said circuмcision didn't justify.

CHAPTER I.
 On the Inability of Nature and of the Law to justify man.

The holy Synod declares first, that, for the correct and sound understanding of the doctrine of Justification, it is necessary that each one recognise and confess, that, whereas all men had lost their innocence in the prevarication of Adam-having become unclean, and, as the apostle says, by nature children of wrath, as (this Synod) has set forth in the decree on original sin,-they were so far the servants of sin, and under the power of the devil and of death, that not the Gentiles only by the force of nature, but not even the Jews by the very letter itself of the law of Moses, were able to be liberated, or to arise, therefrom; although free will, attenuated as it was in its powers, and bent down, was by no means extinguished in them.

Voilà:
https://www.papalencyclicals.net/councils/trent/sixth-session.htm

. . . not even the Jews by the very letter itself of the law of Moses, were able to be liberated, or to arise, therefrom . . .