Many people come across as angry to others even though they deny that they are actually angry.
Sometimes, this may be due to not being aware of how angry you actually are. (You are angry, but don’t realize it, or you don’t want to admit it)
Alternatively, the problem may be that your body language indicates anger to others, even if your words do not. If this is the case, you need to pay much more attention to your body language so that you are more aware of how others are seeing you (and consequently reacting to you)
Start with your voice tone. Is it friendly or threatening? Is it intimidating? Is it pleasant or irritated? Is it loud to the extent it could be mis-interpreted?
Your voice tone communciates much about your emotions. Being more aware of how it is affecting other people is an important step in managing anger and also in becoming a more effective person. Try putting a “smile” in your voice and see if people don’t see you as less angry- and respond to you accordingly.