OK, that's not gonna end well, you'll probably sceptically freak out, but I think these christians in some sense are right. You have heard this argument 100x before, you think we, as a highly organized and compicated system can exist as a result of a coincidence, because of a chance. There is so much molecules, that there are possible combinations which allows an existence of life.

But this is not a question of a chance. It's a question of enthropy. Enthropy is a force of chaos, it smoothes differences (like energetic) in a system, disorganizes it. It's commonly seen as an effect of decay. All living organisms can survive only because they fight with the enthropy all the time, they multiply their cells and individuals, they read, repair and copy their DNA all the time, without a rest, this is the only way how a DNA information may be preserved. A cell is designed to do this purposely, to preserve and multiply itself, except of common functions, like serving as a muscle.

We imagine, that a "primordial soup",  a warm place, rich for water, carbon, sulphur dioxide, and so on, is simply a machine, which first produces amino-acid molecules and then combines them one after another as a brute force algorithm, to break the password of life, to invent DNA and let it multiply. Let's put aside for now how this is coincidential or natural.
This is, when the enthropy ruins the job. Whenever any molecules connects together, there will be always enough of them around, so there will be inevitably another, "wrong" molecule, which connects to it and makes the macromolecule useless. (useless? For what use?)
A basic parts under an influence of enthropia are restricted from forming a higher systems. The only way how to surpass enthropia, is a highly organized and intense activity directed on survival, or no activity at all.
It's impossible for nature to have a protected pond, where a molecule develops, by one correct piece of adenin, guanin, thiamin and cytosin after another. There is theoretically a chance, but it isn't enough for the time of milliards of years we can consider as a reasonable. The life just appeared too quickly. And imagine, how this succesful hit would look under a microscope. Imagine these molecules connecting to one another in a correct order. It would look just like a controlled process. Humans have about 3 milliards of base pairs in DNA. Unfortunately I couldn't find how many a simple bacteria, possibly primordial, can have, but it would be still a lot, for them to be all generated correctly, before a sun of our type would burn out and destroy such a promising place for life.

Even if by some miracle such a molecule appeared, there are no mechanisms how to protect it, feed it, repair it and copy it. This requires a cell, fully equipped by enzymes, cell membrane, mitochondria, vacuoles, DNA coiled into chromozomes, and so on. These things can't multiply without DNA, and DNA can't multiply without them. There is no way how they could appear, sustain themselves and come into unity with a DNA, which of course already must contain an information of their construction.

We know, that some viruses are really simple. They can be created by mere mixing together a DNA solution with compounds for a cell membrane. But viruses are not a primordial form of life. They are parasites on cells, they do nothing by themselves, when they're not in cells. And in cells they just rewrite DNA already present there, to produce more viruses. Viruses wouldn't survive without cells.

All this problem is a variation of the classical "was the first a hen or an egg?" Its solution is a "dinosaur egg", because we know the birds evolved from dinosaurs, but this can't be applied on the life itself. I have heard that a possible principle are crystals, but how can organic, amino-acid molecules, still in a water, become a crystal, is unknown to me.
Of course I still don't consider it as a reason to be a Christian. This thought is relatively logical, but most of the rest of religion isn't.
Please, if there is any mistake in my theoretical mind exercise, feel free to point it out, but I am here, unlike the christian couple who probably won't read all the hateful BS by which you show how nice person you are.
Note, that I usually know nothing of common logical and illogical arguments, until you mention them here and I google em up. 

Summary:
Here is  my argument a considering the life too complicated to appear by a natural cause. The coincidential life creation wasn't yet repeated in a laboratory, and it currently isn't proven by an experiment. This may sound as an argument from ignorance, but just after it I point out the lack of supportive mechanisms, without which a DNA isn't able to persist. Even DNA itself is a complicated structure, like these spinal base molecules, keeping it together, you see, the double helix beauty...

Now it is a typical argument of the fine design. I honestly tried to fix that error, to study this argument and I have found
this link:
http://www.discovery.org/scripts/viewDB/index.php?command=view&id=91 on this argument, so I hope to find there its flaws. But this document is very long and so far there still are just supportive arguments and defeated objections, gotta read further. Or did I really stumble upon a theistic web page? Maybe yes, there are sacred incantations like "quantum/vacuum fluctuation", "pre-existing superspace", or "spontaneously".

This objection is quite interesting.
Objection 4: The "Who Designed God?" Objection
As I would describe the problem, the major difference, between things, which needs a designer (universe) and which doesn't need a designer (God) is a time. If a time is a property of this universe, then this universe has a beginning and an end. The time is believed to start with the big bang, about 10-20 milliards of years ago. If God is independent on this universe, (which we suppose it is) then it is not dependent on a time, as we know it, so there is no  need for God to have a beginning or an end. Note, that physicist still didn't explore the time precisely, what it exactly is, they haven't mastered it, so there is too much of blank space for the atheistic side of the argument. Theists, on the other side, doesn't understand the time either and can just rely on the argument of ignorance, and assume things, thus this objection isn't much objectively discussable.