You say you referred to the Catechism, and your brother resists that, so it’s scriptural references only. But the Catechism and its footnotes are full of scripture: the line of reasoning is scriptural. Which does he care most about: the page the scripture is quoted on, or the content of the scriptural quotes? If he’s willing to read a book, what about that book first of all? I wouldn’t give up easily on the Catechism–the theological support from scripture is given there for both doctrinal areas, and you both would have the advantage of this being the Church speaking for herself as formally and officially as she can, in language geared to our contemporary ears. The communication is direct and not through a third party, which latter, as we know, can muddy the waters. (I.e., if one is going to attack/defend, let it be the strongest and purest articulation of an idea, rather than a straw man.)
Besides if your brother is willing to read Trent, which is the official Church speaking, then he can be willing to read the catechism, which is the same thing in these times.
Protestants who come from this bias have looked at parts of Trent a lot, but without understanding at all. They look only to mock and attack. Since Trent was defending the Faith against the Protestant attack, it is written to that end. It was written going on 500 years ago, to a world whose literate citizens were Aristotelian in philosophy, Thomistic in theology and Catholic in sensibilities. Today’s citizens do not have those literacies, so we cannot assume or even discuss at a Thomistic level. Nor is the polemical purpose and tone any longer appropriate given that those days’ formal heretics are only these days’ accidental or material heretics no longer aware of, nor responsible for, the links broken long ago by Protestantism’s founders. The truths remain true; but emphasis has changed as the times have changed, and doctrines also have continued to be fleshed out and rearticulated for a culture which has lost much intellectual integrity.
My point is, resist arguing Trent. The current articulation (the Catechism) is the appropriate articulation unless this is an archeological or historical discussion. The terms, concerns and principles shared by all western men at the time of Trent are no longer even understood by modern man outside of those versed in Thomism. Defending Trent is easy for those who understand and accept the Church’s authority and teaching infallibility. Defending Trent is neverending when a modern sets out to mock and misuse it.
Your brother’s critiques to you I have heard before: they are current in fundamentalist protestant apologetics. He is getting them from elsewhere and not deriving them originally. The mode is quite biased. This mode limits you to the protestant voice. As I said, I would not just silently accept this mode. If you do accept it, then I would think the best articulations would come from the new teaching Catholics who bring a Protestant sensibility with them. So that’s Scott Hahn and Tim Staples–the clearest and most interesting I’ve heard, and man do they have that Protestant-speak. They each naturally come from scripture thoroughly. Both have books out.
As to the Protestant mode: notice if you take that position to the limit, each bible reader must be proficient in all the ancient biblical languages just for a start. Of course Protestants protest at this extremity, but the logic holds.
Notice that the first Christians, to whom the epistles were written and with whom Acts is concerned, did not have a written New Testament but had the Faith, which illustrates the obvious fact that having the Faith is not dependent on having the written account of the Faith. Just this one historical fact alone suffices to eliminate necessity, so although the New Testament is priceless, it’s not necessary qua written–the teachings in the book are what’s necessary (unwritten teachings also necessary, and the Church as Teacher also necessary). If nobody had ever written anything down, there would still be a Christian Church dating back to Christ. Catholicism would agree with this hypothetical; protestantism cannot.
Just generally, if you push sola scriptura to its own logical limit, not only did it not happen in the story of the New Testament itself; not only is it not mandated anywhere in the bible itself; it is in itself impossible just on paper. Impossible for human beings, who by nature come to know sequentially (unlike angels, whose minds know outside of time).
Although it is truly great, I would not recommend for your purposes Aquinas’ Summa Theologica. You need philosophy to do his theology, and I do not generally find Protestants to be in touch philosophically with the necessary first principles. A whole pre-study would have to be done before theological fruits could be examined. This is a patience that our 2000 year old Church has practiced, but the individual Protestant, alone in his theological universe, doesn’t have the inclination, tools, intellectual customs, or time to start where the beginnings are.
But if you want to bring Thomas Aquinas in, I might suggest his Summa Contra Gentiles. It is written less formally, more for the layman, and is just wonderful.
Blessings on you and your conversations with your family members. Hope this helps.