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Well, first of all, I do not see the warrant for either word to carry the plain meaning of "abolish." That said, you are certainly right for distinguishing the difference between these words, they are different words. They have similar meanings, but they are not the same word. Matthew uses a slightly stronger term which the BDAG renders "to end the effect of." But Paul's use of καταργεω carries the meaning "to make powerless."
In the end, I do not see the contradiction in context. But I think that the nuance of the terms can assist in making clear the intentions of each.
Remember the context too, He was constantly being accused of disregarding or breaking the Law...when in actuality He was the only one to have ever truly kept or fulfilled it.
Also, in order for there to be a true contradiction (concerning the law of non-contradiction) He and Paul would have had to meant what they stated in the same sense, the same manner AND the same time. In one time (His time until the cross) His purpose was not to disregard the law but to actually fulfill it on our behalf, then in the later or another time (the cross) He was to abolished it or nail it to the cross with His body.
I am beginning to look at other uses of the words in the NT. Both words are used in contexts where "abolish" just does not make sense. καταλυω is used in Luke 9 to mean lodging - presumably because you can "down loose" your robes once you are in a friendly place, rather than "girding them up" for travelling. As my wife says to me if I leave my coat on inside, "Are you staying or not?". So in this sense Jesus says he came not to "undo" the law. καταργεω is used in the parable of the barren fig tree in Luke 13 where the tree is "using up" the ground unproductively. There certainly seems to be a difference, and I will meditate on it some more. Thanks.