Why do people assume being an atheist means you don't have morals?
Because they equate religion with morals. History shows that to be false
Because they are ignorant. Then again, we can ask why religious people who are force fed moral behaviors don't follow their teachings.
Most religious people have been taught their whole lives that their sense of morality comes from their god via their religious texts and religious leaders' interpretations of those texts. It is so firmly embedded in their psyche that morality comes from their faith that they honestly can't fathom any other source. There are exceptions to that, of course, but since your question was a generalization, so is the answer.
They can't accept that atheism is a considered position, as that would obligate them to entertain the possibility it could be right, at least for some people. So they assume that it involves some combination of hatred, anger, licentiousness, dishonesty, confusion, hopelessness -- ANYTHING so long as it's negative and evil. OR since everything in their world involves religion, they assume it's a sort of anti-religion or a religion with the god of self or some such.
In short, they try to make it SAFE and RELATABLE to themselves. At our expense.
Also, fundamentalist Christians especially care about BEING right rather than DOING right. Being right is Job One. And atheists, as the polar opposite of credulous adherence to religious faith, must be a wrong as it's possible to be.
So ... don't expect their heads to stop exploding at the very thought of us.
You'll do somewhat better with liberal Christians and some iconoclastic "spiritual but not religious" types. But in general, you're not going to win respect from most theists.
Theists are high on religion, so naturally they think it is impossible to live without it.
Because christians have to have their book to keep them from killing and raping, and even that doesn’t work.