The ArgumentThe cosmological argument is extremely old but has been reused and modified many times.

The basic Platonic/Aristotelian cosmological argument is this:

Every finite and contingent being has a cause.
A causal loop cannot exist.
A causal chain cannot be of infinite length.
Therefore, a First Cause (or something that is not an effect) must exist. God is then often inserted as this "First Cause".

The newer more often quoted Kalam cosmological argument is this:

(1)Everything that has a beginning of its existence has a cause of its existence.
(2)The universe has a beginning of its existence.
Therefore:

(3) The universe has a cause of its existence.
(4) If the universe has a cause of its existence then that cause is God.
Therefore:

(5) God exists.

The Kalam cosmological argument is the one most often used in contemporary debate by apologists such as Dr. William Lane Craig.

Problems with the various cosmological argumentsThere are some major flaws and logical fallacies in the arguments:

THe biggest flaw in the argument is that it does prove anything, but instead replaces the supposed problem with a larger problem. If the universe was made by a god because nothing can exist without cause, then something must have "caused" God.This is often countered by saying that God is the exception to the rule, however if God is the exception to the rule why cannot the universe be the exception to the rule without God.
The original argument is non-specific: It states there must be a First Cause but doesn't say that the First Cause had to be God or a divine being. There are an infinite number of causes other than a human-inspired god that could have caused the creation of the universe. The creator of the universe need not even be supernatural, or sentient or intelligent to satisfy the argument of "first cause".
The argument makes the assumption that a causal chain of events cannot be infinite, that it must terminate at a point. While the nature of cause and effect is observed by experiment (within the limits of the uncertainty principle at least), whether this chain can be infinite or not is certainly not mandated by experiment and is only inductively prefered.
It forgets the fact that matter and energy necessarily exist and are not contingent: The 1st Law of Thermodynamics and the Law of Conservation of Mass state that matter or energy cannot be created, nor destroyed. Therefore, there cannot be a state where matter or energy does not exist. Because of this, matter and energy necessarily exist. Therefore, this argument doesn't apply to matter or energy.

Dr. William Lane Craig's Wording

Dr. Craig words the argument like so:

(P1) Everything that begins to exist has a cause.
(P2) The universe began to exist.
(C) Therefore, the universe must have a cause.

Dr. Craig then claims that God did not "begin to exist" but instead has always existed and that his argument is therefore not a logical fallacy. The problem with that however is that it makes the assumption that God was the first cause, that God didn't begin to exist, that the universe did begin to exist, and the biggest assumption of all that God exists which the argument doesn't prove. It ignore scientific hypotheses such as the cyclical model which posits that the universe is in an infinite loop of big bangs followed by big crunches and therefore doesn't have a beginning.

I can make the same argument and say that Unicorns are that first cause.

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