Here's an easier argument that lands in the same place: if you roll your own crypto, and it breaks, you will look incompetant. Everybody will ask, "why didn't you just use TLS?", and your answer will be "so I could write this custom protocol that just destroyed my security!" On the other hand, if you use TLS, and someone asks why, you will simply say "because if TLS fails, people are going to target the banks and stock exchanges before they target my service."
For the record: you have Colin Percival on HN suggesting that hand-rolled crypto beats SSL. Colin's a smart guy who really knows crypto.
You also have Thomas Ptacek on HN suggesting that Colin is absolutely full of it. Thomas isn't as smart as Colin, but, on the other hand, Thomas has been breaking software professionally since 1995, and has more crypto findings than Colin.
Make up your own mind.