I was being facetious there. Doesn't always come accross well online.
But you have actually highlighted a reason why he doesn't tell friend!Lavellan:
'Only have him divulge this very earth-shattering secret to someone who has proven willing to listen'
Solas has trust issues and his only friends for the last goodness knows how many thousands of years have been spirits. Since he woke up he's been shunned by Dalish clans and treated as an apostate and second class citzen. He has really bad trust issues.
And he has no idea how Lavellan will react to this news. Solas is very careful in what he tells people and the only people he lets close are Cole and his girlfriend. The secret he has is huge. It could utterly destory some Dalish because it takes away everything they believe in. Solas shares it with Lavellan because he trusts her. Because he wants her to know the truth about himself. Maybe that seems harsh for a Lavellan who is only a friend but - here's the important part - they are only a friend. I consider this to be perfectly in character for a man who has massive trust issues and a habit of being very careful with what he tells people.
tl;dr: I have a lot of thoughts on this subject. Some of them are starting to make sense.
This is why I said that this scene could have been tied to the approval system, like Sera's roof cookies or Vivienne's formari ring scene. Both of those scenes are often hard to get, since both require a very high friendship. To even get to a high rating, you have repeatedly demonstrated to Solas that you are not one of the hostile Dalish who would react in the same manner.
That being said, you bring up a valid point. You can still be a friend (aka have positive approval) but not be enough of a friend to have Solas' confidence. He does have trust issues.