I actually just now took the time to read some of their rationale for choosing May 21st. Interesting.
They are basing this date off of the time of Noah's Flood, add 7000 years, and then factor in some verses in Revelation that talk about a specific period of days of silence. Also, according to their calculations, it ties in significantly (numerically-speaking) with the exact date of Jesus' death.
It's quite good, in its own way.
I still doubt they're right, particularly based on some of their other beliefs, but it's at least interesting to read.
But, if I'm not here on May 22nd, then I'll be eating crow in heaven. And, really, I'm okay with that.