Reads more like logic for thee but not for me...
Which part is illogical, in your view? The conclusion, or the statement that the first cause must be eternal? Because the latter is bullet-proof.
Again, by definition a first cause is uncaused. If it was caused, then it wouldn't be the first cause.
If the conclusion is what is illogical to you... then please esplain yourself.
The alternative is an infinite regress of causes, which is not only absurd and goes against Occam's razor, but according to many philosophers, is logically impossible.