Abide means to be able to live with, or stand. If you can't abide with something, it means you can't stand it. If you can abide it, it means you can live with it.
An old definition of abide is 'to live'––think of abode, as in dwelling. If you abide by the rules, it means you live with them, and you will follow them. If you can't abide your sister's shrill violin playing, it means you can't live with it, you can't be in the house when she's practicing. You abide something you don't like, like your teacher's long stories about math. It's not a pleasant experience, but what choice do you have?
v put up with something or somebody unpleasant
experience (emotional) pain
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accept, live with, swallow
tolerate or accommodate oneself to
hold still for, stand for
tolerate or bear
take lying down
suffer without protest; suffer or endure passively
take a joke
listen to a joke at one's own expense
endure to the end
bear (a cost or penalty), in recompense for some action
get one's lumps, take one's lumps
suffer the results or consequences of one's behavior or actions