[shagie]

As I understand it, this has to do with who was asking for a thing and what they wanted.

The upper class spoke French and when they asked for beouf, they wanted meat, not a cow. Likewise when they asked for poulet, they wanted a cooked chicken, not a live one.

The lower classes spoke German and gave us cū (kuh in modern German) for a cow and cīceb (Küchlein in modern German) for chicken.

As English grew from both of these roots, the different words remained.

[jgtrosh]

Don't let Shia fool you, it's bœuf.

[Eremotherium]

Almost: Küken means chick. Küchlein would be the diminutive of Kuchen (cake) so a small cake or sweet pastry.