Okay, I have a number of points to address before I move onto the OP.
First: Atheism states nothing as to what your beliefs actually are. It merely states that you are atheistic. This is derived from the pre-fix "a" which means not or without; and theism which means: Belief in the existence of a god or gods.
So "atheism" literally means: not or without the belief in the existence of a god or gods.
This tells you nothing about what I do believe, and rather what I do not believe. Saying "I am an atheist" would be like responding to the question: "What do you do for a living" by saying "I am not a doctor." There is no standard by which people who are not doctors live their daily life. There is no standard by which people who are not doctors make a living. All that you can gather from that statement is that they are not doctors. Just as all you can gather from the statement "I am an atheist" is that, that particular person does not have belief in a god.
With this information I can confidently state that atheism does not contradict itself in it's beliefs as atheism is the lack of a belief. If you wanted to argue whether or not atheistic-naturalists (or any other type of atheist that well .. has a belief) contradict beliefs that is an entirely different topic, one which I am not discussing right now. Atheism is not a religion. Atheism is not a set of beliefs. Atheism is merely the lack of believe in a god / gods.
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With that settled I shall move onto the original poster:
You want to dispute Christian (specifically Catholic) arguments; I have spent a long time doing this myself. I find there are a number of approaches, and you should choose which will work best depending on who you are debating with.
The first argument, that is / was common to atheists, and is very well known, easily disputed but if the person is not philosophically inclined, it is a very solid argument:
A- If a being is omnipotent, they can do anything.
B- God is omnipotent.
C (Given a and b)- God can do anything.
D- If God can do anything, he can perform X.
E- Let "x" equal: create an object, too heavy to lift.
Therefor, given C, D and E, God can create an object, which is too heavy for him to lift.
I think you can see the problem here: If God can create this object, he cannot lift it, therefor, not all powerful. If God cannot create this object, he cannot and therefor, not all powerful.
People often argue to this argument "God can do anything that isn't a contradiction to everday reality: Doing something he can't do contradicts itself". This is a valid argument however:
There is nothing contradictory with:
Y can do X.
There is nothing contradictory with: Y can do X when X = create an object too heavy for them to lift.
If you insert human into "Y" in this case, it would be true. I can create an object I cannot lift. Therefor, it is not a contradiction until you insert an omnipotent God. This is because omnipotence contradicts itself.
That is known as the omnipotence paradox, you can read more:
http://en.wikipedia.org/wiki/Omnipotence_paradox
The second approach I like to take is the literal vs. contextual interpretation.
As you and I both know, Catholics claim to read the bible "contextually"; whereas there are other branches of Christianity who may take the other stance on this (Literally.)
Now; reading the Bible contextually, I have a problem with this. Since a Catholic interpretation of the Bible will take the majority of the Old Testiment as symbolism, but then literally believe that the New Testiment (Jesus' life, The Gospels, etc.) actually happened. How can a "mere-human" pick and choose which parts of the "divine-scripture" actually happened, and which are meant to be symbols? If you want to read contextually, you better believe that the whole Bible is really just a symbol, as anything can be taken symbolically. However, catholics will not happily admit that the whole Bible is contextual, because then that opens up Jesus for attack. If however, you get them to agree with this, and take a literalist interpretation, open up your handy dandy bible, and read the first 2 stories of Genesis. I think they will find a nice contradiction when God created the world ... twice?
Contextual reading was developed to get around this (and the many other) contradiction(s) in the Bible. However, just by taking a contextual stance you open yourself up for attack as humans are choosing what the symbols mean, humans choose what is symbolic, and even Catholics will attest to: humans are not perfect. Therefor, they would have to also agree that it is possible humans made a mistake. Therefor, it is also possible that Jesus is just a symbol for water; and this "God" is really just a symbol for oxygen; if humans are reading "in context" humans could have easily created this context.
If the above argument didn't make much sense, I apologize. It was thought out by me, and I still don't advocate it very well. The third argument I will give is:
Omnipotence contradicts omniscience.
That is to say, nothing can be all powerful and all knowing at the same time.
Take an example:
God knows what will happen, when it will happen and how it will happen. That means, he knews in 2 weeks today he will part the red sea.
Does god then have the power to not part the red sea?
If he is able to not part the sea, he did not *know* correctly. That is to say, his omniscience were incorrect, as he did not part the red sea two weeks from today, and that makes him not all knowing.
If however, he is not able *know* incorrectly, he is not all powerful, as he does not have the power to oppose his omniscience.
Again, this argument can be brought down; however, it works decently well.
My final point is not actually an anti-theistic argument:
It is illogical to believe in God, as there is no proof of this. Until something is proven, there is no sense in believing in that. You would not believe in the magical cupcake floating around the galaxy of andromeda .. until I proved it to you.
Now they may see "Well there is no proof against god either", to which you reply "Burden of proof is in the hands of that person making a positive claim. Take my magical cupcake. Is it logical to believe in it, merely because you cannot prove that is does not exist? No. Why is God any different?"
Because of this point, do not concentrate so largely in making claims against gods existence, merely dispute claims people make for it. Because until an undisputable claim is made, it is illogical to believe in it.
I hope this was helpful; and legible. I am tired as I type this, so not sure how well I am conveying my point. But yeah! Best of luck!