I have always approached this subject the wrong way. I looked for rules in scripture. I lamented that scripture is never clear about the composition of "the households." (Taken as purely circumstantial evidence, the household passages favor the infant baptism position. The scripture identifies the head of the household as the believer, and never mentions that every adult member of the household made a credible public profession of faith.)
Credobaptists will understandably point to verses that teach the sequence: believe and be baptized. These verses, on the surface, support the practice of credobaptism.
Of course, it is always true that one can never be certain that the professing adult is sincere in his testimony. Even more insidious, he might be sincere (actually believe) and still not be saved. Such is the case, for example, of Simon the sorcerer.
Nevertheless, we can accept that scripture teaches: believe and be baptized.
What it does not teach is that a public profession of Christ is necessary at the time of baptism.
And, more importantly, and what took me a while to appreciate, but which now seems obvious is: scripture does not teach that infants, even those in the womb, cannot be believers.
After all, as the case of Simon the sorcerer demonstrates, as well as the demons in the book of James, and the rocky soil types, that simple intellectual assent (belief) is not enough. One must be regenerated. One must be given a saving faith in Christ.
Such a person, one who has been regenerated, believes and should be baptized, regardless of whether they can articulate their belief.
If we believe that any children who die in the womb or in infancy are saved, then they must have been regenerated. They were "qualified" for baptism, and yet many churches would deny them that privilege.
Would there be children baptized who were not and would never be saved? Of course. Just as there are adults who are not believers and yet are baptized.
If you believe children should not be baptized, I wonder how you deal with the following situation. In the next age, you meet a fellow saint. She tells you that she died at five days old. "How were you saved?" you ask. “By faith in Christ, just like you, of course,” she replies. Then she adds, "By the righteousness of Christ I was reborn before physical death, sanctified, and made perfect. Though a sinner for the short time from conception to death I was able to stand blameless before a holy God. But, apparently, I was never qualified to be baptized in your church."
Believe and be baptized is correct. Assuming that infants can not be believers is wrong.
Yet You are He who brought me forth from the womb;
You made me trust when upon my mother's breasts. (Ps. 22:9)