he doesn't. Dukkha is a hard word to translate, it's a bit closer to "attachment".
Buddha tried living without any material goods, like many other hindu spiritual leaders, and found that it did not work.
His revelation is that of the middle way; not getting rid of everything, but not becoming attached to anything.
You don't get rid of everything that causes craving, you get rid of craving. Then having isn't a problem - it's only a transitionary stage, and need not be feared or loved.
But, to believe in Buddha, one must believe that one is capable of ataining enlightenment by one self.
honestly, that is a solid point. I find that Buddhism is helpful even before one reaches enlightenment; it is not a required part of the method. However, it is certainly taught as a requirment, so you have a valid argument there.
There is a similar issue with the understanding of karma and re-incarnation. If you follow the fundimental teachings, karma is a central pillar of the Buddhist philosophy. But if you don't believe in reincarnation, then karma as defined is meaningless.
I have found that little is lost by removing re-incarnation from the Buddha's teachings, but my doing so is certainly an example of my selective reading.
Everything has its weaknesses.
"If you meet Buddha on the road, kill him".