Is apologizing a weakness?

It's just something that has been on my mind lately. I said some rude things to a female friend of mine and she said that she doesn't want to be my friend anymore. I'm planning to meet her in person tomorrow and apologize to her but something tells me she'll just see me as weak and desperate so I prefer not to do it. She was one of the greatest persons I've ever met and I just want things to go back to the way they were between us. What do you guys think? Is apologizing a noble thing to do or does it just reek of desperation?
Is apologizing a weakness??
Is apologizing a weakness?
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