What is Philosophy? How Does Philosophy Relate to Irreligious Atheism?

Philosophy comes from the Greek for "love of wisdom," giving us two important starting points: love (or passion) and wisdom (knowledge, understanding). Philosophy sometimes seems to be pursued without passion as if it were a technical subject like engineering or mathematics. Although there is a role for dispassionate research, philosophy must derive from some passion for the ultimate goal: a reliable, accurate understanding ourselves and our world. This is also what atheists should seek.

Atheists, too, are often accused of trying to strip passion, love, and mystery out of life through relentlessly logical and critical arguments about religion. This perception is understandable, given how atheists can behave, and atheists should keep in mind that even the strongest logical argument doesn't matter unless it's being offered in the service of truth. That, in turn, requires some passion and love for truth. Forgetting this can lead to forgetting the reason why you're discussing these matters at all.
A further complication is how the Greek sophia means more than the English translation "wisdom." For the Greeks, it wasn't just a matter of understanding the nature of life, but also included any exercise of intelligence or curiosity. Thus, any effort to "find out" more about a topic involves the attempt to expand or exercise sophia and thus might be characterized as a philosophical pursuit.
This is something which atheists in general should develop a habit of doing: reasoned, critical inquiry into the claims and ideas around them as part passion for learning the truth and separating true from false ideas. Such "disciplined inquiry" is in fact one way to describe the process of philosophy. Despite the need for passion, that passion needs to be disciplined lest it lead us astray. Too many people, atheists and theists, can be led astray when emotions and passions have too much influence over our evaluation of claims.

Seeing philosophy as a type of inquiry emphasizes that it is about asking questions — questions which, in fact, may never actually get final answers. One of the criticisms which irreligious atheists have about religious theism is how it presumes to offer final, unchanging answers for questions to which we should really say "I don't know." Religious theism also too rarely adapts its answers to new information that comes along, something which irreligious atheists must remember to do.
In his book A Concise Introduction to Philosophy, William H. Halverson offers these defining characteristics of questions which fall within the field of philosophy:

• They do not fall within the competence of any of the sciences.
• It is genuinely difficult to determine what kind of evidence, if any, is relevant to answering them.
• They are logically fundamental.
• They are questions of broad generality, questions whose answers have far-reaching consequences for our understanding ourselves and our world

How fundamental and how general does a question have to be to call it "philosophical"? There is no easy answer and philosophers don't agree on how to respond to that. The characteristic of being fundamental is probably more important than that being general, though, because these are the sorts of things which most people usually just take for granted. Too many people take too much for granted, especially in the realms of religion and theism, when they should ideally be asking questions about what they have been taught and what they simply assume to be true. One service which irreligious atheists can provide is to ask the sorts of questions that religious believers don't ask of themselves.

Halverson also argues that philosophy involves two separate but complimentary tasks: critical and constructive. The characteristics described above fall almost entirely within the critical task of philosophy, which involves posing difficult and probing questions about truth claims. This is precisely what irreligious atheists frequently do when it comes to examining the claims of religious theism — but it's not enough.

Asking such questions is not designed to destroy truth or belief, but to ensure that belief rests upon genuine truth and is genuinely reasonable. The purpose is to find truth and avoid error and thus to aid the constructive aspect of philosophy: developing a reliable and productive picture of reality. Religion presumes to offer such a picture, but irreligious atheists have many good reasons for rejecting this. Much of the history of philosophy involves trying to develop systems of understanding which can withstand the hard questions of critical philosophy. Some systems are theistic, but many are atheistic in the sense that no gods and nothing supernatural is taken into account.

The critical and constructive aspects of philosophy are thus not independent, but interdependent. There is little point in critiquing the ideas and proposals of others without having something substantive to offer instead, just as there is little point in offering ideas without being willing to both critique them yourself and having others provide critiques. Irreligious atheists may be justified in critiquing religion and theism, but they shouldn't do so without being able to offer something in their place.
In the end, the hope of atheistic philosophy is to understand: understand ourselves, our world, our values and the entirety of existence around us. We humans want to understand such things and thus develop religions and philosophies. This means that everyone does at least a little bit of philosophy, even when they have never experienced formal training.

Neither of the above aspects of philosophy is passive. Whatever else might be said about the subject, philosophy is an activity. Philosophy requires our active engagement with the world, with ideas, with concepts, and with our own thoughts. It is what we do because of who and what we are — we are philosophizing creatures, and we will always be engaged in philosophy in some form. The goal for atheists in studying philosophy should be to encourage others to examine themselves and their world in a more systematic and coherent manner, reducing the extent of errors and misunderstandings.