What's illogical about the analogy?
Well, for a start, that watch did NOT come to happen in a quick explosion. We had the explosion and it took about 11 BILLION YEARS of things coming together to make that watch happen!
Moreoever, while the creation of life took the larger first part of those 11 billion years, once it happened things were no longer entirely random. Some things work better than others once the groundwork has been prepared. Once mankind came on the picture, things started to develop at a HUGELY faster rate! We went from sundials to inventing that watch within a couple of hundred years, because there were all sorts of people all over the place busy inventing and developing all the pieces necessary to make that watch.
This is MUCH different than your analogy paints!
There are other points to argue as well but those aren't the real issue anyway. It's been my experience over the years that those who favour Intelligent Design are guilty of trying to have things both ways, eating their cake and having it too. That's just illogical.
Why do I say that? First of all, virtually all of them are not just trying to prove the existence of God. Whether God exists or not is irrelevant to how the Universe came to be and how it works. It is what it is and we may never be capable of understanding all of it. The existence of God is not necessary to explain it. He may have started it all off or it may have been random chance. The result is the same.
No, what the proponents of Intelligent Design seem always to be pushing, once you scratch the surface of their arguments, is a literal acceptance not just of their Faith but of their interpretation of their Bible. They don't just want God to be accepted as real and the Creator of the Universe. They want it accepted that he did it the way THEY say He did! No evolution, no dinosaurs, just Adam and Eve chomping apples in some mythical garden.
This idea of telling God how he did his works has always struck me as incredibly arrogant and presumptuous! A bunch of people barely out of the caves, wearing skins and scratching their asses come up with some stories to explain how the universe came to be and a few thousand years later their descendants are still taking it as truth and gospel!
If someone wants a discussion solely and only about the possibility of a Prime Mover I could enjoy it. What I can't abide is someone who really just wants to use that idea to get his foot in the door to justify his collection of tribal myths and fantasies that outright contradict the evidence that Science keeps discovering every day!
Science does not contradict ANYTHING on how a God may have created the Universe and set up its Laws of Operation! The only contradictions are with what some people chose to believe in ADVANCE of those discoveries!
To put my own views more succinctly Betsy, although I personally am a 'devout agnostic' I can get along with someone who believes in a God just fine!
What I can't abide is someone who rejects the continuing unfolding of evidence as to how the Universe began and endures because he feels that his simplistic little book of myths has given him all the answers, somehow making it unnecessary for him to actually learn any Science, Math or Physics!
It's no shame to be ignorant or math challenged, but it is a shame to use some prop to be arrogant!