Why does she care? It's not like you rejected her publicly or anything. It's not like people will go to her page and see, "Aren't we adorbz? -- with EMPTY VOID" and silently wonder when the dissolution of your relationship began. It's not like you symbolically broke the digital bond of affection you shared. And for what? Because you have a slight case of stoned-face?
I'm just kidding, James Franco. Of course you can untag yourself. We've all done it. There's no need to apologize or send a "I may have untagged myself on Facebook, but not from your heart" Hallmark card. Facebook is sacred. It's the place where we can pretend we all lead glamorous social lives and that we've never had terrible lesbian haircuts or worn tie-dye jeggings. To take that right away from someone is uncouth.
I'm surprised she noticed, frankly. Usually you can just quietly click the remove-tag button after a few days and no one is the wiser. It's a passive-aggressive, unphotogenic person's dream. Untagging yourself from a photo in which you're part of a couple is dicey territory, however. But, assuming you don't always untag yourself from couples pics, you can appeal to your girlfriend's own sense of vanity in this situation. Show her an unkind photo you have of her (and I'm sure you have one) and ask her how she'd feel if that was aired for her whole digital world to "like" ironically.
When in doubt, it is always nice to ask someone if they mind being tagged in a photo. Some people are really
weird sensitive about that, even if it's something innocuous. Plus, you never know. Maybe they were lying to their girlfriend about where they were and your pic just blew their cover.
Here are a few other tagging rules, because we're on the topic. Don't tag photos of people who aren't in them just so they'll look at them. Yes, that's a really pretty picture of quinoa salad, but I don't want that shit on my wall. Unless it's a pun. Then maybe.
Also, does the person in the pic in question have more than one chin? If so, don't tag. Are they holding an illegal-looking substance? Don't tag. Your case of spliff-face counts here as well. You can always tell your girlfriend something about professionalism and credibility and blah de blah. If they look like they recently had sex or ran a marathon, don't tag.
To spare yourself future embarrassment, Facebook does allow you to control what happens when friends tag you or your content, or post on your timeline. If you want to see and approve a photo or comment before it's shared on your page, you can do so by going to privacy settings > timeline and tagging > edit settings.
Did I miss anything? When do you think it's acceptable to untag photos?