At first, you were strongly attracted to each other -- and this attraction probably blinded you to what are some very basic differences between you. As time went on and the dust of the initial attraction settled, you may have started to realize that you are, in fact, quite different, and you have two really different, maybe even opposing moral codes. This won't necessarily mean you are arguing all the time; it could occur on a minor level and just lend some irritation to your interactions -- or maybe even some welcome stimulation!
However, it could be a lot more serious than that. If you're both feeling as if you're extremely different on a basic level, you probably won't be progressing as a couple as well as you should. It's natural, if unfortunate, to look at differences as a threat. You might start looking at each other as a stranger rather than your close, intimate friend. You might even wonder from time to time why you're together, which is a valid question to ask. After all, are you looking for a partner in a romantic relationship, or are you looking for someone who will serve as a counterpoint to your own personality, someone who will hold your interest even as they get under your skin -- over and over again? If you're looking for a true relationship, this relationship might not provide what you're seeking. The likelihood is high that you disagree more often than you agree, and that can try even the most patient of souls.