This is a supplementary for the accepted answer.
I wanted to post this as a comment to the accepted answer. But since my reputation doesn't allow me to, I'll post this as an answer instead.
So Basically -
Because he is a Badass Wizard.
There is an interesting question posted here on scifi.stackexchange:
Which of Dumbledore's abilities make him the greatest wizard of the age?Which of Dumbledore's abilities make him the greatest wizard of the age?
The answer with the most votes on that question essentially answers your question. Check it out.