Maker's Breath.... (Official Cullen Rutherford discussion)

It was true that the Chantry took away her child as soon as it was born. It was never going to turn out any other way once she had decided to stay with the Circle. However, that did not mean she was abandoned by the father because she never even told him she was pregnant. It is only assumed that it was Greagoir because he was sent away to Denerim for a year and a half around the beginning of the Dragon Age, which was the right time scale to be Rhys' father. Whilst the Knight Commander claimed it was just that the Denerim Chantry needed Templars, there were rumours it was really because of some sort of transgression.

Whilst Wynne didn't reveal the name of the father to the First Enchanter at that time, Irving who was still just an regular enchanter and Wynne's friend apparently told him it was a Templar and had suspicions about who it might be. I dare say other people realised too, which is why he was sent away. When he returned, he discovered about the birth of Rhys and was very bitter because Wynne never even gave him the option to do anything else. The unsigned letter from the Templar who was Rhys' father makes it clear that he would have fond a way to keep their son. He states he would have given up the Order for the sake of both of them, whereas apparently Wynne had convinced herself that he wouldn't. So in future years that was the line she obviously took when asked about it; the Templar was too in love with the Chantry, the Templar order and beholden to his vows but that just wasn't true.

I think it is sad because presumably she never told Rhys who his father was other than he was a Templar and that only came out when she was drunk.   As Greagoir says, "He was mine too.  The Chantry may have taken him, but you kept him from me."