What does it mean to be "open-minded"?

I had a friend today essentially accuse me of being closed-minded. I took it very personally. I didn't pursue the offense, not wanting to cause more friction, and the subject we had been discussing was dropped like a lead anvil. I've always thought of myself as a pretty open-minded person, but I don't think I realized exactly how important that particular self-image was to me until today.

The thing is, this friend was sharing her views, and I listened to them. Then I started to share my differing views, and I thought I was being very friendly about it. I wasn't attacking her own opinion or practice, just offering a different way of looking at the issue. Almost immediately, though, she felt like she had to defend herself. "Well, I've read a lot of imformation on [the subject]." Well, I had done my own reading on the subject as well, on both sides of the argument. But because I continued to disagree with her, because I had come to a different conclusion, she cut me off. Forget it, she said. "I can tell you're not open about it," so she just dropped it. Well, I followed suit; I hadn't come in the first place to talk about it, and there really was no point in pursuing the subject further. But, if I was not open about the whole thing, she was certainly just as closed as I was, perhaps moreso. I listened to her. She would not listen to me. Well, that's how I saw it, anyway. No doubt she saw things differently.

But then it got me thinking about: What does it mean to be open or open-minded, vs. closed or closed-minded?
Here's what good ol' dictionary.com has to say on the subject:

o·pen-mind·ed  
–adjective
1. having or showing a mind receptive to new ideas or arguments.
2. unprejudiced; unbigoted; impartial. 
— adj  
 having a mind receptive to new ideas, arguments, etc; unprejudiced  
open-'mindedly  
— adv   
open-'mindedness 
 — n  
Famous Quotations
open-minded
"I am open-minded on all questions I care nothing about."

closed-mind·ed  
 –adjective
having a mind firmly unreceptive to new ideas or arguments: "It's hard to argue with, much less convince, a closed-minded person."
adjective 
not ready to receive to new ideas [syn: close-minded] 

So, which was I, on the debated subject? Was I being open-minded? Well, I thought so. I was listening. If my friend had had sources there on hand for me to read, I would have read them.

Or was the mere fact that I already had an opinion enough to disqualify me?

Gosh, if being open-minded means never having an opinion, or never making up my mind, it's really not a good thing, anyway.

Though, I do believe it is conceivable-- and also the most probable-- that I fall somewhere in the middle.