why is it hard to be happy for someone else?

I don't think you should fake emotions. You need time to grieve. Give yourself some time and distance from her until you can come to terms with your pain and sadness. When the pain has lessened, try again and see if you can see past your own pain and see that she is happy. Always be honest and sincere though. Keep it to yourself though, the old saying rings true, "If you can't say something nice, say nothing at all".