People build AS on Xin because his Passive, his Q, and his W both get better with it. That's 3 of his 5 abilities. Furthermore, his W lowers CD on his other abilities based on his AS, meaning it benefits all of his abilities.
People build SotD and Youmuu's on him because the CDR and AS means that he can bring his ult off cooldown stupidly fast, and SotD means that when you pop its active then hit your R it hits with (Armor-30)/(Armor+70) against anyone with 30 or more armor, on top of Youmuu's penetrating 20 and having around 21 with a full set of runes and masteries. Having 71 armorpen means that you'll be hitting your R at full damage (with your undodgeable attacks reducing your cooldowns) against every poor nontank bastard on the enemy team.
Black Cleaver is derp to rush on Xin Zhao; it provides, humorously enough, too much of a focus on pure damage and too little on his other stats. Xin Zhao needs Armorpen, not armor reduction applying to one person over 3 hits. That only encourages you to try putting your armor debuff on people before you swing your R around, which means you're less likely to hit 4-5 people (and even if you do, it'll hit all but one of them more softly).
It's better, in most cases, to get him his SotD, his Youmuu's, a Frozen Mallet, then more surviva so you can make it to the middle of their team and hit your R.