Isn't it disrespectful to our marriage when my husband asks a girl that we've fought about out to lunch?

My husband and I had a fight about him being too flirtatious wit a "friend" of his on Facebook. That was a couple of months ago. Tonight, I find out that he told her that they should go out to lunch sometime. I told him that it's disrespectful to me and our marriage that he did that because this girl is single and probably thinks that we're having problems in our marriage if a married man is asking her out. What's wrong with him that he can't see my point of view?