Here's the scenario...
You're fingering your girlfriend's bum and she's getting hot and horny and she suddenly says "I want to try anal sex", or maybe it's your all your idea and she's so turned on she says "Yes!", so you lube up her hole and your tool and start to push, and push, and it's not going very far so you push harder, and harder and suddenly it pops in! But then she starts screaming "Stop! Stop! It hurts!". And later she says it still hurts. And later she says she wishes she'd never wanted to try it. And later she says she wants to see her doctor. I just about guarantee she will never, EVER want to try it again.
Which is sad, because anal penetration and intercourse can be amazingly pleasurable. (This is true for men too, because it's a unisex pleasure, but that's not the topic here. Hello, pegging, plugging, fisting, etc).
IMHO, it is the duty of the male to be responsible by manually probing and massaging the recipient before proceeding. Unless 3 fingers on one hand, or 2 on both hands can easily be massaged in, do not proceed. Instead, take the opportunity to erotically dilate, massage, and "train" the sphincter to receive... maybe next time.
Keep in mind there are 2 things going on here... first, the involuntary sphincter sees you as a parasitic invader it wants to keep out, and second, there is the maximum circumference that both sphincters can be dilated.
It may take several sessions, but through manual massage you can 1) train the sphincters to stop fighting and just relax "Hey, it's just me, relax and this'll be great!" and 2), stretch the sphincters to be able accept to you.
Make sure to use stupid amounts of lube. There is naturally NONE in there. (Imagine a fat cluster of pleasure receiving nerve endings embedded in fragile tissues with a hole running down the center that theoretically your cock can pass through, and there's no natural lube!) It works best to squirt or inject 20 cc's or so in there. (You can pruchase silly little sex shop "injectors" for this, but even better are inexpensive 60cc cath-tip syringes.)
Once her sphincters can easily accept you, and if there's enough slipperiness sloshing around inside, fucking her ass with your cock will put her in heaven. (I've known women who preferred anal intercourse because they said it was a more intense "fuck".) But if there's not enough lube, or she can't stretch to accommodate, there will be trouble and sorrow.