They don't.
To make sure that we are on the same page, make sure you understand what faith is.
We use science, because it is demonstrably effective beyond all other human tools. Since the overwhelming evidence indicates that it works, it is not faith to rely on it.
Science is fairly accurate by design. Let's say I were give you an inkblot test, and ask you "what do you see?" Most people would answer, depending on the pattern, something like "butterfly" or "face".
That is actually the wrong answer. The answer is more like, "I see a piece of paper that has blotches of ink on its surface, in a symmetric pattern due the ink spreading because of folding of the paper." Our minds understand things on familiar patterns and trends, which can often mislead us.
The human brain is incredibly susceptible to bias, inaccurate interpretation and error. Human memory is so unreliable that it ranks lowest, in terms of evidence quality, in court proceedings.
Thus, things like anecdotes are almost entirely worthless as evidence.
The most important focus of science is to find ways to objectively verify, outside of the human mind, assertions and data - to reduce error and bias as much as possible. That way, whatever answers are generated have a relatively high accuracy.
Sure, other means of accumulating knowledge exist. We could consort with a Magic 8-ball for knowledge, however, the question remains, "how do we know it is accurate?".
Science, as a methodology, is all about ensuring that we maximize accuracy.
Since atheists are intellectually honest, more often than not, and wish to ensure that their beliefs are actually true, they use science because it works.
- Isn't "believing that God doesn't exist" the same thing as "not believing in God"?
- Do you only believe in what you can see, touch, feel, etc?
- Why do you ignore all the evidence around you for a god?
- Where does morality come from, if not God?
- Why do atheists support gays so much?
- Do atheists believe in nothing?
- If it wasn't God, who created the universe?
- Are you afraid of going to hell?
- Why are you so closed minded?
- What is the point of living without an afterlife or god?
- What if you are wrong?
- Can you prove that God doesn't exist?
- Will you admit that there is a possibility of a god?
- Do atheists have faith?
- Where does the meaning, and purpose of life come from?
- If there is no god, how do you explain _______?
- Why do atheists have faith in science?
- Are atheists empty, unhappy people?
- What bad experience made you hate god?
- Where to do you go when you die?
- Do you believe all this came about by random chance or by accident?
- What would it take to prove to you that a god exists?
- Why don't you just sit down and shut up, and let others have their beliefs?
- Why are atheists so angry?
- Aren't you just rebelling against God because you want to sin?
- Isn't it arrogant to say that science has all the answers?
- Wouldn't it be safer to just believe than risk going to hell?
- What is faith?
- Have you tried to believe in God?
- Why did you choose to be an atheist?
- Doesn't you being so against God prove he exists?
- Is atheism a religion?
- Where do you think rights come from, if not God?
- Do atheists want to take religious freedom from Christians?
- What is in it for me to be an atheist?
- Don't atheists believe there is no god?
- How do you know you are right?
- Do you believe in a soul or spirit?
- If you don't worship God, do you worship yourselves?
- What is an agnostic?
- Don't you have to be skeptical about skepticism?
- What is the difference between an agnostic and an atheist?
- What do you base your beliefs from?
- Don't you know that you're just supposed to have faith?
- What is an atheist?
- Why do you ignore god?