Same reason as Christianity.
Both religions have explicit commands in their scripture (which is also expounded by their religious authorities) that require the spreading of their respective religion to every corner of the "world."
These days, xtianity does this using less conspicuous tactics (like hospitals, NGOs, placing influential xtians in top positions in various organizations etc) while Islam hasn't reached that level of expertise &/or cunning.
The best they can come up with is Saudi, Turkish etc funded madrassas and mosques in various countries (from Japan in the East to the US in the West), love-jihad etc. Their other methods are less "palatable."