Faith is not merely an intellection decision, it is a gift from God received at Baptism, and the soul has to have the disposition (continuity of sanctifying grace) to allow the gift to give certainty to the intellect.
This is contrary to Protestant theology which calls for a personal decision to accept Jesus as your Lord and Savior, which is why they reject the idea of infant baptism.
Thomas Aquinas gives us the explanation of the Catholic position in the Summa Theologiae ST II-II, Q6, a1
He begins with a quote from St Paul’s Letter to the Ephesians (2:8-9)
For by grace you have been saved through faith, and this is not from you; it is the gift of God; it is not from works, so no one may boast.
For Paul “works” refers to obedience to the Torah Law, which is a kind of intellectual assent, only certain by maintaining one’s decision/obedience.) Thomas rightly points out that faith is attained in two steps, first matters of faith must be revealed by God and proposed to man. Secondly, is the assent to faith (the acceptance of the matters of faith as truth.)
This second phase may initially be an intellectual decision, but an intellectual assent alone is not enough for certainty. We see this happen as youth mature and are exposed to modern philosophy and a myriad of religions that are seen as an alternative to the religion of their (Catholic) parents. Even mature Catholics waver with doubt which is distinct from inquiry or wonder. (Faith seeking Understanding is not doubt seeking certainty.)
Here’s Aquinas’ explanation in excerpt:
Two things are requisite for faith. First, that the things which are of faith should be proposed to man: this is necessary in order that man believe anything explicitly. The second thing requisite for faith is the assent of the believer to the things which are proposed to him. Accordingly, as regards the first of these, faith must needs be from God. Because those things which are of faith surpass human reason, hence they do not come to man’s knowledge, unless God reveal them. To some, indeed, they are revealed by God immediately, as those things which were revealed to the apostles and prophets, while to some they are proposed by God in sending preachers of the faith, according to Romans 10:15: “How shall they preach, unless they be sent?”
At this point in Thomas’ discourse however, it may seem that the “gift” is revelation itself, and is preached. Still tending to an intellectual assent. It is in “regards the second” that he first touches on the internal supernatural gift:
As regards the second, viz. man’s assent to the things which are of faith, we may observe a twofold cause, one of external inducement, such as seeing a miracle, or being persuaded by someone to embrace the faith: neither of which is a sufficient cause, since of those who see the same miracle, or who hear the same sermon, some believe, and some do not. Hence we must assert another internal cause, which moves man inwardly to assent to matters of faith.
He concludes by referring back to the idea that matters of faith are beyond man’s natural ability to know and therefore man’s assent of faith must be moved by God’s gift of grace, an interior motion to assent that gives certainty to the intellect.
Since man, by assenting to matters of faith, is raised above his nature, this must needs accrue to him from some supernatural principle moving him inwardly; and this is God. Therefore faith, as regards the assent which is the chief act of faith, is from God moving man inwardly by grace.
In the context of the ongoing discourse on Faith and Reason, there are some who do not have the supernatural grace that gives certainty and their certainty can only come from “pervasive quantitative hegemony,” which only gives certainty to those things proven. In the Letter to the Hebrews Faith is defined as “The substance of things hoped for and the evidence of things unseen.” (Heb 11:1) In Romans 8:22 the contrast is made and seems to speak directly to the positivists of today:
Now hope that sees for itself is not hope. For who hopes for what one sees?
You are right in saying they reject faith, a) because they don’t have the gift of grace and b) they want to believe only what is “seen” (proven.) In the context of Thomas’ theology and Catholic belief, the intrinsic (natural) desire for God can only be satisfied by God through faith. However, those who remain unbaptized or those who do not maintain sanctifying grace through the sacramental life, are in a constant state of doubt which requires proof.
To paraphrase from your email, the [call to] “faith is with us for good and it cannot be “severed” from the human.” Faith however is a gift that that once received must be maintained. In other words prior to the gift it is only the desire (which cannot be severed) and the unaided intellect directs that desire toward many things below the horizon of eternity.
ST II-II, Q6, a1