THE OFFENDERS.
Long story short: they get out of control. So, guppies typically give birth to fry every month. Ok, sounds pretty normal. So what? Well...
IT TAKES A MONTH FOR A PREGNANT GUPPY TO GIVE BIRTH. Thats right. A month. Which means these fish can get impregnated again right after they give birth. Is it good for breeding? Yes, but for people who just want a few fish, this is kind of a nightmare. Sure, you can seperate your male and female fish, but get this:
FEMALES CAN MAKE BABIES BY THEMSELVES.
Ok, not entirely true, but they can keep male sperm in them for up to six months, which they can make babies with. Guppies also are able to breed around 6 weeks, and you can tell the difference between male and female guppies at about 4 weeks. Which means, if you aren't fast, by the time you sort your babies, they could've already bred. Again.
On the other hand, this is a great fish to breed. Depending on the breed, they can sell for up to 100$ per pair! They can breed up to 20 times in their life, and make about 1-200 babies per batch.
So, in a nutshell: guppies are great for breeders, not so good for just fishkeeping (unless you're ready to get a bunch of tanks for the sheer amount of babies you're going to have).