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It sounds like a good(attractive) idea (suggestion), but they fail to understand (see, notice
There is probably an element of truth in the arguments (ideas), but they ignore a more important (basic) fact …
Closer examination (analysis), however, suggests (shows) that this argument (claim, idea) may not be borne of (supported) by the following evidence (facts, examples, statistics).
Close (careful) examination (analysis) of these arguments (ideas, suggestions), however, would reveal (suggest, prove) how flimsy (不足信的，不严密)(fallacious（靠不住的）, groundless（没有根据的）) they are.
However logical (sound, forcible(有说服力)) these arguments may be, they don't make sense (only skim the surface of the problem) when … is viewed the other way (taken into consideration).
As opposed to (Contrary to) the widely (commonly, generally) held idea (belief, view), new studies (facts) challenge (fail to justify) the opinion (view).
Good/Superior/Wonderful as …., it has its own disadvantages/ it brings its own problems.
They may be right about …, but they seem to neglect /fail to mention/take into account …
In all the discussion and debate over …, one important/basic fact is ignored/overlooked/neglected.
It is true that/ Admittedly, but it is unlikely/doesn't follow/doesn't mean that …
There is an element of truth in these arguments/statements, but they ignore a deeper and more basic/essential/important fact/factor …
In many cases, however, …
As far as …… is concerned, …
