It was a bit of a journey for me and something I wrestled with, as growing up, I understood Baptism as a public declaration of faith. But what eventually compelled me to change my position was simply God's Word, which describes Baptism with a much richer language than what I had previously been taught.
So, in other words, I think if we read everything the Scriptures have to say about Baptism, the question isn't really why we should embrace Baptismal regeneration, but why anyone should think less of Baptism. That is, the burden of proof is not on those who hold to the orthodox teaching of Baptismal regeneration, but on those who reject it. But the difficulty with this is that we can't simply compare what one church body teaches about Baptism against what another church body teaches. We have to look at their entire theological system and understand how Baptism fits into the different systems.
Very simply, though. I think a strong case can be made from the words of Paul, who says: "When the goodness and loving kindness of God our Saviour appeared, He saved us, not because of works done by us in righteousness, but according to His own mercy, by the washing of regeneration and renewal of the Holy Spirit, whom He poured out on us richly through Jesus Christ our Saviour, so that being justified by His grace we might become heirs according to the hope of eternal life."
And: "Husbands, love your wives, as Christ loved the church and gave Himself up for her, that He might sanctify her, having cleansed her by the washing of water with the word, so that He might present the church to Himself in splendour, without spot or wrinkle or any such thing, that she might be holy and without blemish."