Why should or should not Iago be admired for his skill?
In Othello, Iago should be admired as an archetype (a type of character), but not as a type of person. Iago is Shakespeare's greatest villain, and he has more lines than any other character in the play: the play could very well be titled Iago. So, Iago should be admired for his words, but not his actions.
Iago is a Janus-figure, a two-faced character who opens and closes doors and scenes. As such, he begins the play talking and ends it mute: quite an irony. In between, he is a source of wit, irony, evil, deceit, and morbid jealousy. He is called "honest" no fewer than 25 times, mainly by Othello. His monologues are majestic, especially the one he says to talk Roderigo out of suicide:
Virtue! a fig! 'tis in ourselves that we are thus
or thus. Our bodies are our gardens, to the which
our wills are gardeners: so that if we will plant
nettles, or sow lettuce, set hyssop and weed up
thyme, supply it with one gender of herbs, or
distract it with many, either to have it sterile
with idleness, or manured with industry, why, the
power and corrigible authority of this lies in our
wills. If the balance of our lives had not one
scale of reason to poise another of sensuality, the
blood and baseness of our natures would conduct us
to most preposterous conclusions: but we have
reason to cool our raging motions, our carnal
stings, our unbitted lusts, whereof I take this that
you call love to be a sect or scion.
Overall, Iago is a trickster of the highest sorts, comparable with the biblical Satan, the epic hero Odysseus, and our American rogue-heroes Huck Finn and Holden Caufield. All of them are splendid liars too. However, Iago is a misogynist who leaves a bed full of dead and will be tortured for his crimes. His skill at lying leads only to destruction and chaos.
It should be noted that to admire Iago is something that transpires from an academic or intellectual standpoint. His machinations and manipulations are very well conceived and he understands the motivations of the characters in the play more than anyone else. The argument can be made quite successfully that Iago understands more of human nature and motivation than any other Shakespearean character. All of this being said, I think that Iago cannot be admired because of his lack of human sensitivity. That is to say, one cannot look at Iago as an example of how humans should behave because his actions are demonstrative of deliberate cruelty, actions that cannot be tolerated in any social setting as they delegitimize human connection as opposed to validating it.