I feel sometimes that the but means what you say, but (ha!) esp. in the case of "I've never had an abortion but..." as in "I've never lost someone close to me but..."
The "but" becomes empathic.
But (again, ha!) sometimes people do use it to create a sense of superiority. "*I* would never have an abortion but..."

Exactly. Whether or not the "but" is empathic or disapproving depends entirely on the words that come after the "but". That's why I try very hard not to throw up a mental barrier as soon as I hear the word "but" in this and similar contexts.