Hey there First I would like to point out the obvious; if you guys were together for a year you were pretty serious about each other. That makes this break-up ten times harder then your average break-up. Have you ever heard the saying, that "a clean break is best?" It really is the truth. When you break something all the way through - it will really heal the fastest. Honestly it would probably be unhealthy for both of you to be friends at this point in time.
Do you feel like you are over her and vice versa? When the time comes where you can say that and be dead honest; you probably would be ready for a new kind of friendship with her. If you don't think that you could ever be just friends with her then it is probably better that you just let her be and try to move on. It would hurt less for yourself, imo.
What caused the break-up? Was it particularly nasty and left bad feelings? If any resentment is involved then it would probably be hard for you to be friends in the future. Try to keep things cordial and nice, but realize that things would make both of you a lot happier if you just kind of stayed away from each other until the resentment dies down a bit.
Has she moved on? Have you? Moving on might be the best solution to mend this heartbreak. It has been three months so it's probably time to get back into the dating scene. You should probably avoid a long-term relationship if you remain hung up on her,though.
As for what she's thinking -
Getting into a girls head:
Her not being friends with you really helps her deal with her resentment and makes it easier to get over you. She is probably really trying to make things stay over and the only way she can accomplish so at this time is to not be friends with you. One day when you both really have moved on and gotten over each other I'm sure that she would have no problem being your friend.
I hope that everything works out for you. If you ever need any more advice or find that you have additional questions feel free to either respond on here or send me a PM.
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Antidisestablishmentarianism.