Thank you very much for your comments on this subject.
If the origin is uncertain, how can you know the Apostles taught infant baptism? You can take certainty from what was only passed down orally, until the writers you cite? Tertullian could have been right, but how can you know for sure? I take it that since I'm not the first to ask, that this is what Councils are for.
Men of that era make the claim that the practice originated with the Apostles and their generation. This is something one wouldn't write if there was contrary evidence, or if people knew it was not true. If there was a "rule" regarding baptism that said "only adults could receive" that people knew about during that time, could Tertullian write that it was an "ancient practice"? When we say it comes from the Apostles, we mean it comes from that era of time. We presume that if some teaching is verified by an otherwise Catholic writer of the era, then it comes from the Apostolic teaching. The people reading these writings would have been aware of any false teachings - they had already heard the Apostolic teachings, both orally and written. They would be able to identify whether Tertullian was speaking truly.
This is like someone today writing about President Nixon. People would be able to verify whether Nixon did this or that. Thus, future readers would learn something about Nixon - presuming that the writer was not contradicted by other authors of that era. We don't see disagreement regarding infant baptism.
I take it that since I'm not the first to ask, that this is what Councils are for.
Councils are to verify what is the true teaching in the face of contradictory teachings. Thus, the Council of Trent verified Tertullian and Origen, etc., on the Church's practice of infant baptism in the face of the Anabaptists of the 1500's who were teaching the opposite.
Regards