My thinking goes like this, with some simplifying assumptions. Let's say you have a monolith with 99% uptime that you rearchitect into 5 microservices, each with 99% uptime, and if any one of those services goes down your whole system is down. Let's also assume for the sake of simplicity that these microservices are completely independent, although they are almost assuredly not.
From basic probability, 99% uptime means there is some chunk of time t for which P(monolith goes down) = 1%. But
P(microservice system goes down) = P(service A down or service B down or...) = P(service A down) + P(service B down) + ... = 5%
In reality P(microservice system goes down) < 5% because they aren't independent and the chunk of time in which service A can go down will overlap that of service B. But still, that means the upper bound of the whole system going down is higher than for a monolith.
But microservices are pretty popular, and I'm sure someone has thought along these lines before. One potential rebuttal is that each microservice is in fact more reliable than the monolith, although from what I've seen in my career I am skeptical that's truly the case.
Where's the hole in my reasoning? (Or maybe I'm right. That would be fine too.)