Amino Acids with ionizable side chains

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growingpains

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Why isn't serine's side chain ionizable if it's more basic than cysteine's side chain (which is ionizable)?

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"Another subgroup of the amino acids are those with ionizable side chains. These include: aspartate, glutamate, histidine, cysteine, lysine, tyrosine and arginine." (http://webhost.bridgew.edu/fgorga/proteins/aminoacids.htm)

"There are only 7 amino acids with ionizable side chains" -BR

Well I don't know, but apparently threonine isn't ionizable either and threonine has a hydroxyl group on the sidechain just like serine does.
 
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I've read that no, they're not. Not even NaOH will tear apart ROH's, according to TPR Organic Chemistry.
 
TPR:

An alkoxide ion is a poor leaving group. Conjbase of alcohol, a fairly weak acid pKa 15-19
 
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