YTA

Based on this:

At one moment, I said some words that were interpreted as insensitive, which looking back I can agree with.

So your words require "interpretation" to be insensitive, but his words are taken at face value and plain hurtful, even while he's in his time of need, at which point you still make it about you:

I was depressed that I couldn't be his friend when he needed one most

And this:

I approached him and confessed my disappointment and sadness about what he said. I also said that it would have been nice if he apologized, because my feelings were truly hurt. He was my best friend and I didn't want what we had to be broken.

It is hard to tell if you started with an apology. You called it a confession. What the hell did that sound like? Was it one of those "I'm sorry you got upset when I said [such and such]. I was just trying to say [reworded version of such and such]..."

And whatever you said was followed by a demand for an apology from him?

Sounds like only one person's feelings matter here.