"I don't have a girlfriend. But I do know a woman who'd be mad at me for saying that"

The speaker is specifying that they do not presently have a romantic partner, but they do have a female friend who would be disturbed if they openly acknowledged their single status. This quote is most likely meant to be amusing or paradoxical, as it suggests the speaker is indirectly acknowledging their relationship status while also calling attention to their worry of displeasing their good friend.