This is one of those special cases where you can't simply follow general rules for English capitalization. The names of people are proper nouns, of course, but that doesn't mean every element of the name is always capitalized, any more than every word in a book or movie title is always capitalized. (An example: the movie title "Gone with the Wind". Except for the title's first word, prepositions and articles in the title are not capitalized, while other words are, even if those words are not proper nouns themselves.)
In the case of Arabic names, short linking words in the name, like "ibn" or "bin", are not capitalized. There's no universal rule behind this; it's just the way English readers are used to seeing Arabic names. From
the "Name" section of the Osama bin Laden article:
"The decapitalization of bin is based on the convention of leaving short prepositions and articles uncapitalized in surnames; however, bin means "son of" and is not strictly speaking a preposition or article."
For Arabic names, this issue only comes up when writing them in a Latin alphabet. Arabic script does not have capital letters.
Certain other kinds of names also have noncapitalized elements, for example German ones containing "von", like
Manfred von Richthofen.
Capitalization - Wikipedia has some of the gory details.
While I do think capitalization is a useful feature of English, the details do get damned messy, as the Wikipedia article on capitalization makes clear. People can get into big arguments over this stuff. And practice has changed over time; if you ever read older English documents, you may find lots of Surprising Capitals appearing All Over the Place.
