Each bug has a different set of chromosomes. They each pass down different traits to their children randomly. So each child gets a different set too.
Meiosis is the main cause of this because in the process only half of the DNA is randomly put in each new haploid cell. Also, some genes are crossed over when the chromosomes are in tetrads. So if when this happens in you some of your dad's genes are now on your mom's chromosome. This makes it so you can have different combinations of genes.
Say hair color and eye color are on the same chromosome, and brown eye color and brown hair color are dominant traits and all other colors in both catagories are recessive. If your dad has brown hair and brown eyes on one chromosome, and green eyes and blonde hair on another, and he passes on the first chromosome, then your only possibility is brown hair and eyes. But if traits are crossed over, so green eyes and brown eyes switch, then (provided what mom passes on) you have a chance to have green eyes. Otherwise brown eyes and hair would always come together.
Also because there is always a 5o% chance that a chromosome will be passed on, new traits are always appearing in children.
As you can see in these pictures, old colors are kept in the family. First there is only brown, then blue and brown. Next purple, pink, blue, and brown. And finaly, pink, yellow, blue, orange, white, purple, and brown. And not all of my bugs look the same. Two are brown, one is green, and one is yellow, all but one has wings, and three are boys, and one is a girl. Yet some traits stayed the same for all of them like all of them have dots, and all of them have red eyes. Just like in humans, Reebops share some traits with one parent and others with the other parent. Some traits can be shared with none. With my yellow bug, neither parent was yellow, they just both had the trait.