Interesting idea about ICHB about ambivalence towards sex itself, Peter!
I, myself, would not close off other interpretations, but my personally preferred reading is that he is basically sexually open and available to anyone, to "anything you'd care to leave..." It's gotten to the point of being a silly put-on, but I do enjoy his panto about being some kind of desperate(ly lonely) slut overwhelmed with polymorphously perverse desire. The self-hating, self-defeating story of being able to have whomever he wanted but rejecting those who show interest a la Groucho Marx (I wouldn't want to belong to a club that would have me as a member) is old, but it goes on.
I've posted a couple of times (
here and
there) about an impromptu banner I made (out of a table cloth) at a concert: I wrote "We can have both", hoping that he would play it -- and he did on the next tour leg, a month and a half later, making it a tour staple. He was very coy, pretending he didn't know what the song was about. He asked me what "We can have both" meant and added that he's English and "therefore absolutely stupid" about the meaning of it. I retorted that it meant whatever he meant by "I Can Have Both" and asked him to explain himself, which he declined to do. My concertmate holding up the banner with me shouted out, "Special request!"
Mozzer's live show adlibs around this song are especially amusing. I liked it when he quipped that the song was merely about ice-cream -- that he could have vanilla AND strawberry -- that he didn't understand what all the fuss was about!
I have been to
the shop that never opens, an actual place that inspired the song according to a big nose who knows. And I have seen Morrissey a couple of times at this place -- but sometimes I avoided Morrissey when I saw him there because he looked like he was in a foul mood (I was wrong, but oh well). It no longer exists in that location as it did in the mid-90s.