I understand the declension of что --  it's inanimate/неживой, so of course it should be

Nom: что
Acc: что
Gen: чего
Dat: чему
Inst: чем
Prep: чём

Likewise  кто is animate/живой, so it should be

Nom: кто
Acc: кего
Gen: кего
Dat: кему
Inst: кем
Prep: кём

These are basically just modified versions of the standard masculine adjective declension pattern (somewhat like the declension of "день" -- the nominative is irregular, but everything else is normal).

But if что is inanimate, then shouldn't also "ничто" be inanimate/неживой? And yet "ничто" always seems to be declined as if it were *animate*/живой (кто and никто don't have this consistency issue, for example).

Specifically, I have noticed that 

"ничего"

is almost always used for the *accusative* form of ничто, even though I would have only expected it to  be used for the genitive form. 

Can someone help me?