There are millions of Christians on the planet and I have no doubt that you could find some that use that logic. They would be in error when they do.
Of course your lumping together of all Christians and all christian thought based on your experience with some is equally absurd.
But let's address the things that are wrong with that argument as well as your analysis of it.
First it assumes that all things have a cause. This is generally our observation of the universe but it is not proven. So much for the empirical method and all of science which is based on it. Without assuming causation nothing can ever be proven. What are we to do? Obviously we must assume this as the first part of the sylogism but we must never forget that it is an assumption. With this assumption we can formulate all the laws of nature and adopt the scientific method and draw conclusions. What we can't do is state our conclusions are 100% firm and when talking about the fringes of human experience, like say the beginning of the universe, or the existence of God or the supernatural, then we can't even say that our conclusions are even remotely firm.
The second assumption is that there cannot be an infinite regress. Logically this is completely without support. There is no logical reason to assume that there cannot be an infinite regress. All of the best observations that we make about the universe lead us to believe that it had a beginning but those too are based on the assumption that everything has a cause. In general, I subscribe to the idea that the universe had a cause and that there is not an infinite regress, as do almost all cosmologists, but I admit there are assumptions involved there.
Now let's put that syllogism together:
If there is causation
and if there is no infinite regress
Then there had to be a creator.
We should all note that the form of a syllogism always includes the assumptions clearly stated and preceded by the word "if". In this case it would be better written if it said "then there had to be a creation."
What that creation was would have to be answered with further evidence or further syllogisms. And as long as we have admitted that empiricism is an assumption then God as creator is just as rational an explanation as any other. Unproven to many but nevertheless a rational explanation that can and should be explored.
Now for me that is not an unproven explanation since I have experienced God. For many others that is also not an unproven explanation since they have experienced God too. For those of you who have not experienced God, or are unaware of it, I cannot prove it to you but I can suggest that you stop trying to disprove what cannot be disproven as that is silly.
While the first argument is probably something that you have seen people argue the second is not that common and more likely you have misunderstood what people were trying to say.
It is true that God's existence cannot be disproven but I personally know of no one who uses this to conclude that his existence is proven.
Again it appears that you are laying out bad arguments that can conveniently be discredited for the purpose of discrediting Christianity. It is a shame for you that discrediting one or two or three illogical Christians does nothing to discredit Christianity as a whole.
Might you be desperate?
