I recently found the above graphic on Tumblr. It attempt to show how Christians often commit logical fallacies. I think it is important to recognize that some of the examples are truly bad and should not be used. Others need to be understood. Let's look at each one and see if the examples make sense.
"Everything has a cause but God"
The reason why non-believers think saying such a thing is special pleading is because they think that God is like every other created thing in existence and Christians are merely trying to assert that we can think of God as a special case. This is not what Christians are advocating. If God was a created being, then who ever made God would be God and worthy of worship and glory. The buck has to stop somewhere or you have infinite regression. The universe is not eternal but had a beginning therefore it can't be UNCAUSED.Something or Someone came before it. That cannot be avoided or ignored. Dr John Lennox dealt with this problem.
"Jesus suffered on the cross to save you miserable wretches from eternal torment."
I don't see this as playing on emotions. This is just telling the truth. Not one of us is more of a wretched sinner than anyone else. We have all failed to meet the standards of God and your own. That is undeniable. Someone has to pay for that. You can pay for it in hell or you could accept that Jesus paid the penalty for your sins on the cross.
Knocking Down Straw Men:
"Evolution is like a hurricane assembling a fully functional 747 from parts."
What we have here is a failure to communicate. The way evolution is now understood and explained is not chaotic chance driving the evolutionary process. This is why it's bad idea to raise this argument. It is a straw man. The analogy does not work.
Stretching the Truth
"Those trapped miners were saved by a miracle from God."
Such a statement stretching is not stretching the truth. In order to make that charge, you have demonstrate that the saving of the miners was not miraculous and that God did not do it. That is not possible.
Running From Contrary Evidence
God created the universe, so it can't be 14 billion years old.
The Bible does not say that the universe is not 14 billion years old. This is another argument Christians should not use.
The True Christian.
Those atheist arguments don't have any effect on me.
I do not see how this argument says anything about true Christianity. The reason why atheistic arguments against God would have no effect on a believer is because they are bad arguments.