Catholics have long held that household baptism meant infant baptism, but it actually disproves infant baptism. Hear me out on this one. The Greek words and Hebrew in the scriptures make a distinction between family (genos) and household (oinia). They arent the same words and mean different things. Neither require infants but household often excludes infants by active verbs that infants can't fulfill.
Family includes infants in most cases when used generally, but household does not. Greek and Hebrew can use household to exclude infants as well. The word household defeats infant baptism rather easily. Don't let Catholics deceive you.
Consider Genesis 15:3 where Abram had no children of his own, but he did have a household. He had no seed at that point but one of his household was heir. So, household can be without infants and doesn't mean family. It is common for Catholics to argue households often had infants, but what they really mean is families had infants. It was common for infants to be in families, but household doesn't mean family and excludes infants.
Another example is John 4:49-54, Jesus healed a son of a man who had servants separate from his family, and it says his household believed. They were old enough to believe and not infants. The word household is economic, those participating economically, such as servants. Household does not mean infants who do not cooperate or participate in economic interests. Infants benefit but do not actively participate in shared economic endeavors. Families without infants can participate in households, Heb 11:7 calls Noah's family a household, but there are no infants in that household, only 8 adult souls are meant. Abraham and Noah both demonstrate households without infants, and Noah's baptism did not imply infants since there were none.
And Abram said, Behold, to me thou hast given no seed: and, lo, one born in my house is mine heir.
We see that Abrams house did not contain a child of his own, but he did have a household. This is true of eating the passover in Exodus 12. Eating was divided into households and counted for sacrifice numbers by those eating. Infants don't eat lamb. So, infants were not included in the term household. We see this in the Lord's Supper and breaking of bread in Acts 2:40-47.
Acts 2:41
Then they that gladly received his word were baptized: and the same day there were added [unto them] about three thousand souls.
Acts 2:42
And they continued stedfastly in the apostles' doctrine and fellowship, and in breaking of bread, and in prayers.
Acts 2:43
And fear came upon every soul: and many wonders and signs were done by the apostles.
We see those baptized were those receiving the word, they also broke bread and continued in doctrine, thus not infants. It becomes obvious infants aren't included in the household of faith. Infants do not fear from miracles as in v.43.
The eating of the passover in Exodus 12 excludes infants, they killed lambs for each household but were numbered according to who ate. Infants were not in the numbering as they did not participate in eating the lambs. This is common when applying the word house or household, especially where action is required and practiced. Consider the story of David and Mephibosheth, where Ziba had fifteen sons and twenty servants. They were to till the land so that Mephibosheth and his son could have food. see 2 Samuel 9:10
It is obvious that the word household would exclude infants since they cannot plow the land or bring in the fruits, yet they are referred to as a household. see v12
and all who lived in Ziba's house became Mephibosheth's servants... So we know it didn't mean infants who aren't servants in an actual sense. Infants are family, but not servants, and not part of the active household.
Baptism simply excludes infants who can't consent and take an active part, a condition of Galations 3:26-29 in putting on Christ.
Consider I Corinthians 1 where a household was baptized and the same household ministered. The verb application shows no infants are meant in baptism.
1 Corinthians 1:16
And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
1 Corinthians 16:15
I beseech you, brethren, (ye know the house of Stephanas, that it is the firstfruits of Achaia, and [that] they have addicted themselves to the ministry of the saints,)
So, the multitude of examples we can see the household references didn't include the infants, even if infants were in their families.
One example is Lydia who little is known about her household. Yet it does appear the house was baptized the same location they prayed by a river. This would mean her household may have been female servants who would be with her praying and without men if living with her, so possible no infants were in Lydia's family or household. Since she had her own house Lydia likely had no husband and with no husband no infants in her family.