Ironically enough, "someone who likes math but hates arithmetic" isn't a self-contradictory thing. It's actually a perfect description of a pure (that is, professional) mathematician!
Evidence: look no further than the infamous "Grothendieck prime" 51....
<boldly updates wikipedia>
But, hey, I probably won't make that mistake again. Probably.
I didn't even realise anyone would expect there to be a relationship between "liking" arithmetic and actual mathematics. I worked with mathematicians and was called one myself (it was a stretch, I think) but I have no idea who in the lab was or was not proficient in doing numeric calculations by hand. It was just not relevant. There was one guy though who liked to show off doing things like multiplying long numbers in his head, which was amusing.
It would suck to lack the ability to manipulate algebraic expressions efficiently, but you could go quite far without it in many branches. My most interesting results were identifying certain topological features of certain discrete structures of relevance to biology. There was no arithmetic or algebra involved at all except to write down the results formally.
(To me, 57 is too obviously 3 less than the obviously-divisible-by-3 60.)