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?
The answer with the most votes on that question essentially answers your question. Check it out.