Do you have a strained relationship, or are things not getting along so well with them? If this is the case, then this is an easy reason to explain why you might be having dreams where the two of you are arguing. There is an unsettled dispute going on between the two of you and your mind is trying to come up with a way of coming to a resolution while you are asleep, so that your subconscious can take over the reasoning issue.
When you are dreaming that you are arguing with nobody in particular or are argumentative for no real reason, this is indicative of you feeling angry at everything in general. This is a poisonous attitude which is known for being extremely unhelpful in social situations. Have you been more prone to outbursts than usual in the past few days, or have you been obnoxiously cruel to those around you for no real reason? Think about why your temper is getting shorter and then you may have the answer for why you are dreaming about arguments.
Our dreams come from familiar places. If you have been driving for the past ten hours, you will probably have dreams about driving. If you have been driving for the past ten hours and having visions of your future wedding then you may dream that you are driving towards your own wedding. Therefore, it follows that if you have been in a terrible mood lately and have been treating others horribly, then of course in your dreams you will be arguing with and yelling at others.
Do not let yourself fall into a routine of terrible attitudes. You need to be able to control yourself, because if you cannot explain your actions to yourself or why you have been acting angry for no reason, it shows a definite lack of self control.
Another reason that you might be arguing in your dreams though might have nothing to do with the identity of the person you are arguing with. This interpretation has more to do with feelings of inner strife and issues related to your inner thoughts. If you have been having convoluted thoughts or have been confused about what direction to take a decision in lately, then this could relate to your dreams about arguments. You are dreaming about arguments because you have been having an internal argument with yourself all day long. You should not let things like this seep into your dreams, but because you cannot control these instances, just take a dream like this as a sign that you should take more control over yourself instead. Learn to accept past decisions because it is the only way to move forward.