What is an atheist?
The terms atheist, agnostic, and theist all have multiple definitions and the ones frequently used by believers don't always match those that are often used by atheists. This can lead to very non-productive conversations as the parties involved simply talk past each other.
An atheist can be somebody who believes that there is no god but many, if not most, atheists don't use it that way. Instead, the term just means soebody who does not believe that there is a god. The difference can be subtle but it is important to understand that they often are not claiming to know that god does not exist but only that they have not found any reason to believe that one does. Atheists typically come to their atheism by applying skepticism and critical thinking to the claims of religions and finding them lacking.
Many people will argue that a position of not being convinced either way is what the word agnostic means. That is a valid use of the word but agnostic can also mean somebody who believes that we can't know if a god exists or not and it can also be used to indicate the level of confidence in the position. In the latter use it would mean that an agnostic atheist would not believe in any god but would not claim certainty while an agnostic theist would believe but also not claim certainty. By contrast, a gnostic atheist would claim to know that no god exists while a gnostic theist would claim that one does.
The thing that atheist never means to a non-believer is somebody who is mad at god or who just doesn't want a god to exist. If somebody thinks that there is a god then no matter how they feel about that they believe and that means theone thing they are not is an atheist.
The bottom line is that the best approach is to ask people what they believe or how they define themselves and then take the discussion from there. Arguing about definitions and telling somebody who self-identifies as an atheist that they are "really" an agnostic doesn't move the discussion forward if they are just using a different definition.