It's regrettable that I often come across philosophers who decry Eastern philosophy for it's "lack of rigour", or who find fault with the lack of argument*. After deciding to undertake a concerted study of Eastern philosophy it quickly became apparent to me that here lay two very different modes of engaging in the work of philosophy. In a nutshell, misunderstandings come down to quite different methodological approaches which uncover truth in two different respects. What stands as truth in one mode does not stand as truth in another.
With this considered, it is easy to see why a "Western" philosopher may disregard Eastern philosophy as nonsense, because the way to truth in which the Western philosopher typically moves is different. There is no premise-conclusion structure. Claims seem merely to appear on the page.** In lieu of an experiential connection to phenomena, thought relies on cognition to deliver us to truth. When confronted with this situation we begin from things which we are reasonably sure are true and then produce the logical consequences of those things in order to discover further truths which we are not independently sure are true. A claim which simply stands on a page can lead us down neither route.
Much philosophy which comes from what you might call a broadly "Eastern" perspective lays great emphasis on practice. And by that I mean it is much closer to what you might typically think of as the development of a skill such as painting rather than aptitude in largely cognitive operations. In Eastern philosophy a great deal of effort is made towards ammending one's way of being (gardening, walking, practicing sitting meditation, etc.) As far as I can explain it with words, the basic idea is to stop your racing thoughts because the ways in which we habitually think are too hasty/shallow or simply block us from seeing a phenomenon which we're attempting to perceive. The central claim is that learning to calm these thoughts can alter the mode of your perception in such a way as to open you up to different kinds of insights, unable to be appreciated in other modes.
Instead of offering arguments or providing evidence, then, the business of this kind of philosophy gets underway in inviting somebody to see for themselves by practice. In this respect there is hope for mutual understanding: our shared respect for concrete experience. And I can tell you that it is possible to discover truths in this way, but I cannot hope to convince you of that. What I do know is that you will never be able to appreciate the truth as disclosed through such methods by reading words off a page. And that is why they don't present arguments.
Another unfortunate misunderstanding of Eastern philosophy is that because it cherishes "ignorance" that it is for stupidity and laziness. But again, this comes down to a failure to appreciate the different modes in which one can discover truth. It is not what we think of as ignorance which these methods espouse, but rather having too much knowlege and not enough understanding. The idea is that one becomes more ignorant the more knowledge one acquires. Knowledge can give us access to truth, but too much knowledge can prevent us from seeing the truth. It's simple enough to appreciate this and doesn't even require hours of skillful stillness under a cherry blossom! We can all recall times when we got in trouble by hanging onto too many beliefs about how things are, disregarding what was before our eyes. This popular dismissive understanding of Eastern philosophy is arguably one such case.
* I am well aware that there is a body of argumentative philosophy in India, China, and elsewhere - I do not aim to defend these philosophies here, and all references to Eastern philosophy should be taken to refer to the various forms of what is perhaps shortsightedly described as "mystic" philosophy. I am also aware that many of these "mystics" did engage in public discussion (Chuang-Tzu would often wind up Hui-Tzu, for instance), but the work is not to be found solely or even primarily in debate.
** This criticism often lands on the doorstep of many Western philosophers. I have heard it said of Nietzsche and it is certainly not uncommon to find this said of Martin Heidegger's work. There are well documented similarities in methodology between Eastern thinkers and the particular stream of Western philosophy in which Nietzsche and Heidegger stand. This short essay can stand as a defence of those philosophies as well.