Building Irelia as a tanky dps is the way to go... anyone who says otherwise is playing a champ that is probably not very useful to their team past the 30 minute mark, whereas if you build tanky dps you can carry your team to win and absolutely DESTROY the enemy carry.
Good Build (Cookie Cutter):
ArPen Marks + Quints, Armor Seals, MR Glyphs
Spells: Ghost + Whatever
1v1 Top: Crystal + Pots, 1v2 or 2v2: Dorans shield
Lvl 1 boots
Sheen -> Triforce
Merc treads (Only thing better than CC reduction is more CC reduction)
Build atmas and BV at your disgression... always take a health crystal first though even if you're building atmas.
From there evaluate the situation and start building things like FoN for MR (the movespeed is oh so sexy) or Randuins for Armor.
The reason you DONT need to build irelia as a glass cannon should be obvious, bladesurge. If you're smart, you'll be bladesurging to the enemy carry and smacking them with EQ strike right as the fight starts, and taking them down easily afterwards, who needs tons of AD/AS to kill a carry? Also, this build is entirely tanky, but also has high mobility (triforce) and some AD (triforce + proc, atmas).
One good tip to use with irelia is be sure to combine your ult with triforce mid fight, if you get a swing in every time you cast a blade your damage output goes way up.