Can assuming something that is not true can can be considered arrogant?

i think it can be considered that

Making a false assumption is only arrogant if the person making the false assumption imposes their false assumption on others.  Arrogance is about believing your opinion is the only one that matters.  Arrogance is not about having a false opinion.  

It could.

But as you've chosen not to tell us a syllable more, how do you expect us to say anything actually helpful?

It depends on the context from which it was said.

This could be considered arrogant if the individual commanded an exaggerated or inflated sense of their own knowledge, leading to the assumption something is untrue because this clashes/goes against their belief system.