Well, of course "what I learned in catechism class" automatically qualifies as doctrine rather than argument. But if Christ removed the barrier of sin, then what is baptism for? I have no doubt that, according to the doctrine involved, baptism depends on Christ's sacrifice, but this does not tell us why baptism is required at all.
And of course none of it answers the basic question of why a door needs opening at all.
Not entirely a propos of your post, but I married an ex-Catholic, and what she learned in catechism was dismally deficient. Not only did they miss huge amounts of what is in the Bible, but she managed to get through many years of catechism and confirmation utterly ignorant of many key points of Catholic dogma. Now I realize that you are rather more a student of the subject than that, but I feel it necessary to remark that out of context, "what I learned in catechism class" does not always amount to much!