He claims to start with one assumption, but actually starts with many. For instance he implies "any species which could colonize the galaxy, will". I don't accept that all possible intelligence would try to take over the galaxy.
He also says that it's not in an alien's interest to leave one planet (Earth) just in case we develop - but he doesn't consider that they might have colonized the galaxy but left Earth precisely because they did find life on it. Even the slightly unimaginative at times Star Trek had the idea of humans only colonizing 'empty' areas and leaving anything with existing life on it alone.
Also, he states that colonizing the galaxy takes ~110,000 years because humans took 10,000 years to evolve + 100,000 years to cross the galaxy. He completely ignores that humans actually took many tens of millions of years to evolve from scratch not from existing life forms.
Also, he assumes zero chance of catastrophic accident leading to exctinction as an explanation for why aliens might not exist. Maybe they did exist but wiped themselves out.
Also, he assumes 100,000 years to cross the galaxy, but that means traveling pretty much at the speed of light, which is currently not possible/forseeably practical. Yet he doesn't consider how aliens would stay as a coherent civilization when a light speed ping response starts taking years, let alone tens of thousands of years.
Also, he doesn't consider any kinds of future technology, IT, AI, singularity or similar. Maybe any culture which gets a thousand years past where we are now does not become a galactic conquerer, but a Matrix-style virtual reality.
Lastly, what if aliens decided the best way to colonize the galaxy was to spray terraforming machines and life seeds, and we are the 'alien' intelligence colonies? Who says alien ideas of 'colonize' have to be like human Earth colonies of the last thousand years?