This is called the "Anthropic Principle," the idea that the universe looks like it was designed for life. This logical fallacy is known, variably, as a "False Analogy," or "The Watchmaker Fallacy" a "Teleological Fallacy" or a "Homunculus Fallacy/Infinite Regress Problem" I will explain the origins of each title:
1.) False Analogy: The person in question is trying to compare the universe to an object (a chair, watch, computer, etc.) that has been designed by an intelligent creator. The analogy does not fit because it makes the assumption that complexity must have been designed. There is no known physical law that states this much be the case, and indeed fails to take into account the vast and wonderful process of Natural Selection. Natural Selection, in fact, can cause complexity to arise out of simplicity, by virtue of complexity in many being more adaptive. It takes only the smallest of mutations, and if that mutation is adaptive, it will stick around. If the mutation is a tiny tiny tiny bit from simple to complex, so be it. That happens to, and we have a wealth of evidence showing it.
2.) Watchmaker Fallacy: Best debunked by Richard Dawkins in his book "The Blind Watchmaker," a Watchmaker Fallacy (a more specific version of the False Analogy) asserts that something that appears designed must have had a designer. Dawkins, demonstrating a plethora of evidence to the contrary, asserts that if we can consider life to have been "designed" by a "watchmaker" then the watchmaker had no foresight: humans can choke because our air and food pipes are so close together, we get back problems because we weren't originally meant to walk upright, we have vestigal organs like the appendix, tail bone, and pinky toe. There would be far more efficient ways to design a living creature if there were intelligence behind the design; evolution, however, only selects for what is good IN THE MOMENT, not looking ahead. It is, in that sense, a "Blind Watchmaker."
3.) Teleological Fallacy: Teleological refers to an argument concerning an endpoint, which is a misleading way of looking at things. You can look at the human arm and say "we have an arm because we were MEANT to have an arm in the end" (this would be teleological because it deals with the endpoint) or you can deal with more immediate reasoning, more of the Blind Watchmaker stuff; we have an arm because adaptations towards having an arm were advantageous in that evolutionary moment.
4.) Homunculus Fallacy/Infinite Regress: Originally referring to a "homunculus," a small little man in one's head watching a "screen" projected from the eyes (often interpreted as being a soul or something similar) it unfortunately begs the question of how the HOMUNCULUS is seeing. Does he have eyes? Does he have a head with another homunculus inside watching? If so, there is an infinite regress, a logical impossibility. (As a fun aside, cognitive psychologists and cognitive neuroscientists have resolved this dilemma by pointing out that vision is simply the way in which we interpret light signals. Vision is comprised of brain activity. The conscious part of our brains are made up of how we interpret brain signals. We "see" because that is our method of representing light waves in the visual spectrum.)
Applied to the creation of the universe, if you say that something complex MUST have had a designer, consider the following: Any being who can design an entire world must, himself, be very complex. If complexity REQUIRES a designer, then the world's creator, also, requires a designer. Luckily, complexity does NOT require a designer, so we can leave the "creator" out of the picture altogether. Natural selection does the job nicely without anything supernatural.