What's so important about "sharing a common ancestor"? It doesn't say anything about the spread of different types of life that could evolve, considering we have a sample size of one, and it also says nothing about how difficult it is for any particular form to evolve intelligence.

Because there are probably an uncountable number of different turns life could have made instead to lead to dramatically different outcomes. Life iterates on itself. Mutations on top of mutations. Mitochondria could have just as easily never been enveloped by our eukaryotic ancestors and life would look a hell of a lot different today.

Having a high cardinality of permutations doesn't say anything one way or another about the probability of life arising. it's just hand waving.

I’m not arguing about life merely arising. I’m arguing about the unlikelihood of our idea of intelligence.

"merely" arising. As if it were a simple process itself. Couldn't your argument be applied to either?

Knowing physics is roughly same every where in the universe, same rules of biology will apply elsewhere where if conditions meet, maybe earth is one of many conditions that can form life.

Within those rules are a lot of things that can get by under them. Take two points in earths history bound by the same physical laws and life can look dramatically different. You can think of it like how we all use the same microsoft word but that doesn’t lead to the same exact book being written independently twice or more often. The amount of permutations to be taken along the way is a countless number probably far larger than the number of habitable star systems in the universe.

There's no reason to believe that because the physics are the same the biology will be the same. that's a big ungrounded assumption.