Reduction of amide with LiAlH4 In reduction of carboxylic acid with $\ce{LiAlH_4}$ the first step is deprotonation.

But in the mechanism of reduction of amide with $\ce{LiAlH_4}$ (here), the first step is addition of hydride on carbonyl group. Why doesn't the hydride ion abstract a proton from $\ce{-NH2}$? Since acid base reactions are faster than nucleophilic addition.
As compared to the carboxylic acid, deprotonation of the amide is negligible. 

I don't recall any data for THF or 1,4-dioxane as the solvent, but F.G. Bordwell has determined a lot of $pK_a$ values in DMSO.

In DMSO, the $pK_a$ of acetic acid is 12.6 [1], while the $pK_a$ of acetamide is 25.5 [2].