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I guess it's because Bradley is a human with a transplated philosopher stone. The other Homunculus were born by father, while Bradley pretty much got it put into his human body IIRC.
That doesn't work, because Lin got his stone the same way, but he is able to regenerate his wounds. In the chapter, where Bradley explains his past to Mustang, he says that all that was left was one soul and the feeling of wrath, if it is his soul or a soul from the stone he doesn't know.
I'm not sure, if this is the right explaination, maybe someone can clarify it?
And when it happened with Ling he got the whole package deal, all the souls with the Philosopher's Stone. He didn't kill all the other souls because he made a deal with Greed before the process that happened with Wrath started.