Argue = berdebat, beradu argumentasi, membantah, membuktikan, etc.
Argue has many meanings. It depends on the context.
If two (or more) people argue over something OR two (or more) people are discussing a topic and there are different opinions/ideas --> argue = berdebat / adu argumentasi.
"Cekcok" can also be used in this context, but it is usually used for the daily conversation (not formal writing).
However in this sentence, "I argue that this is impossible because ....." --> when someone expresses different opinion/idea --> argue = membantah / membuktikan.
So, in your context it will be: Saya berdebat / cekcok / beradu argumentasi dengan dia semalam / tadi malam tentang .......