Logic alone

It has always struck me as a little odd that theists use logical arguments for the existence of their god at all. Although it is notable that those arguments have always been found to be based on faulty logic, that I shan't pursue here. Even if it were granted that those arguments were logically sound, I'd still argue that it is insufficient grounds for belief in the existence of anything at all, let alone god.

Reasoning alone is insufficient - Evidence is another critical criteria that should be fulfilled before belief is reasonably warranted.

A logical argument, if correct, only shows that the entity in question may exist. Emphasis on "may" - It has merely demonstrates that the entity should theoretically be in existence. But it does not demonstrate that existence of the entity itself.

If the logical argument alone, without any evidence in favour of it being presented, is sufficient to warrant belief in the existence of the entity being argued for, how is any different from arguing something into existence (ie, irrational).

Furthermore, in case for the existence of a deity, it does not even inform what sort of properties such an entity has (other than the ones within the argument itself). So this makes even odder when theists jump straight for the conclusion that that god is their god.

Take the cosmological argument for the existence of god for example:
1. Every finite and contingent being has a cause.
2. Nothing finite and contingent can cause itself.
3. A causal chain cannot be of infinite length.
4. Therefore, a First Cause (or something that is not an effect) must exist.

If you accept the argument to be true (which I don't), it has demonstrates nothing about the existence of any gods.

So, there is a First Cause. So what?
The identity of that First Cause is unknown.
The current state of existence of it is also unknown.
The properties of that agent is also unknown if it is still in existence.
Any attempts to link the First Cause to any specific deity known to humanity is tenuous at best.

The same goes for all the alleged logical arguments for the existence of god.

No evidence.