Why does "man" command disappear?

I doubt we'll ever be able to tell you where it went, but you should just be able to reinstall it using yum.

yum reinstall man

yum doesn't check to see if files exist when you run yum install, it just checks a database of which packages have been installed. If someone deletes all the files outside of the package manager, it won't know (you can get it to check, but it doesn't by default). Using yum reinstall tells it to do the install even though it thinks the package is already there.

Depending on what has been deleted or removed, you may need to yum reinstall ... other things like man-pages.

Updated in light of new information:

For some reason, your /usr/bin/man is a directory, rather than a single file, and judging by the content it looks like someone has done something weird like mv /usr/share/man /usr/bin or something odd.

You're not going to be able to simply undo this - you need to investigate, see what's been broken or moved, and correct it.

You might just be able to remove /usr/bin/man and its contents and then re-install man and man-pages using yum but without more investigation it's not going to be clear.