a) The bible says and implies this - which therefore makes it a required belief.
b) Humans have evolved the ability to seek patterns, even if there isn't any.
c) Some sense of order exists in the world - and for some this requires explanation.
From the Catechism of the Catholic Church
The world: starting from movement, becoming, contingency, and the world's order and beauty, one can come to a knowledge of God as the origin and the end of the universe.Without being able to find patterns in nature we would never have survived in the wild. Patterns in nature include the seasons, the moon, the stars, tracks in the sand, etc. Knowledge of these helped early crop growers, find water sources and develop primitive science such as tool making. The downside is finding patterns where none exist and giving wacky explanations to accompany them - whether we look into the clouds or stars and see images or hear things that go bump in the night. Some might say they are just harmless and are a healthy part of peoples imaginations, until they are taken seriously and we are required to consult the skies to know what kind of day we are to have or worship the sun.
Only since the advent of modern science have people been able to explain order, this time in terms of mathematics based on simple models. Seasons are easily explainable when one considers the Earth is tilted on its axis and orbits the Sun. There is no need to invoke imagery of death (winter) and re-birth (spring) which formed the basis of what today is known as Christmas, which was hijacked by the Christians.
God botherers like to evoke the supernatural as an explanation to order. For example they say that life cannot come from non-life - this implies God made life as there is no naturalistic explanation. Apart from being a logical fallacy, a false dichotomy, the truth of the matter is that there is no barrier to a naturalistic explanation for life coming from non-life.
When I was young and self taught myself chemistry in high school, I used to believe there was a difference between life-stuff and non-life-stuff. For example, the stuff wood (life) is made of is different to the stuff graphite (non-life) is made of. Learning that they are actually composed the same stuff - atoms, molecules, etc changed my perspective on things. Of course I never had an explanation for what this non-life stuff was...In some sense what I believed would have been little different to what the ancients might have believed about the nature of "stuff".
Arguments from design break down when one considers natural order which can be produced from chaos. This includes cyclones/hurricanes and crystals. We don't need to suppose a supernatural or even natural cyclone maker or crystal designer - we have nature and it's laws which are able to do it with no effort - just time. Emergence from chaos is a fascinating modern study in mathematics which has applications in ecology, quantum physics and artificial intelligence studies. These ideas in combination with the existing pieces of the puzzle (ie the creation of amino acids from basic elements) leads me to believe abiogenesis (life from non-life) is not simply plausible but has likely happened numerous times over the universe.
So what does this have to do with the Illuminati?
Well I'm not actually talking about the group of people known as the Illuminati, but those who believe there exists groups of people who are in control of this world. (ie Conspiracy Theorists) To me they are suffering the same kind of delusion the creationists are - they are perceiving order in the world when in actual fact there are just blind natural forces at play or just patterns in the noise.
What makes people who believe in the Illuminati different is that they are seeing order and intent in groups of humans and across groups of humans and claiming there are people "behind the scenes" pulling the strings and conspiring (perhaps to take over the world). This is similar to what Adam Smith's claimed drove the efficiency of capitalism, the "invisible hand" which controls free markets. Interestingly these patters are suppose to have come from independent humans with different wills but still results in patterns people want to make a story to.
There is a fine line between seeing patterns in a scientific, objective sense - and combining it with another powerful mind trick the confirmation bias...
Personally I see no evidence of agency or intent in the universe or within groups of people. The burden of proof has not been met. This is not a positive claim, but a dismissal of those who claim otherwise. Those who make the case of agency in the universe, and this agency is Jesus have the burden of proof - one which I believe has not been sufficiently met. Similarly those who make the case that the Illuminati are trying to set up a New World Order also have the burden of proof - one which I reject. It's perhaps no coincidence that many who believe in the Illuminati also evoke Christian apocolyptic themes.
What would the world look like without Jesus or the Illuminati? Well - exactly the same!