All airlines offer direct booking facilities on the internet
but the problem is that they only offer you a route flown by themselves
and their alliance partners. This is not necessarily the shortest,
quickest or cheapest route.
Unless you are taking a simple one stop flight it can become a
challenge to book on the internet and may be worth your while
to rather deal with a reputable travel agent.
There are also a fair number of travel sites that specialises
in searching the internet and offer you all the available options.