I have always figured it takes a minimum of 3 pups sold to just break even, IF everything goes well. One covers the stud fee. One covers the other costs related to the breeding: brucellosis test, progesterone testing to time ovluation, travel expense too and from the stud. Then one covers the ultrasound, feeding, vetting and general care of the dam through pregnancy and her and the pups until they leave for their new homes, vaccinations, wormer, litter registrations, microchips, etc... If something goes awry, like needing a C-section or something whacky like the Albon resistant coccidia we ran into a few litters ago that required almost $1000 in meds to treat the pups before they could go home, then it takes more pups sold to cover just the litter costs.
Additional pups in the litter are technically "profit". Though if one figures in the countless hours spent researching dogs and pedigrees to find the right stud, interviewing potential customers, pulling an all nighter for whelping, and then properly caring for the dam and pups, socializing the pups, testing the pups, in the end if it were worked out hourly a breeder is making far less than they could flipping burgers. And of course any pups kept by the breeder, co-owned with others, or who are sold for less than the full amount (maybe a warranty claim by a previous customer) come off that bottom line. And I'm not sure how to figure in all the vacation days from work that are involved in traveling to the stud to do the breeding, whelping the pups and caring for them. If someone doesn't get paid time off work and looses income, that would be a direct cost to doing the breeding. If they do get paid time off work they aren't losing income, but they're blowing all their vacation on dog stuff and never get to take a real vacation from work either.
So yes, if we ignore everything that it took to get the female to the point of being bred and just count the expense vs income for a specific litter than the breeder can make money if it's a decent sized litter. Though I certainly don't think there is anything wrong with a breeder getting some sort of monetary compensation for their time and expertise, it most definitely isn't the driving force behind most good breeders doing what they do.
But then there are often other costs that are directly associated with breeding, though not a specific litter, that we wouldn't be doing if we weren't breeding. I attended the WUSV last fall, which was no small expense. Was it fun? Absolutely. Would I have done it anyway just as a SchH person if I weren't a breeder? No, I probably wouldn't have incurred the expense if not for the opportunity to use the event as a huge research opportunity between being able to see high level dogs from all over the world on the field and spend my days networking and talking to breeders from all over the world to learn from them.
A couple years ago I took several days off work to go visit some stud dogs in the SE. Flew down, rented a car and drove all over 2 different states to see several potential stud dogs I was interested in that were all somewhat close geographically, then flew home. I certainly wouldn't have incurred all those costs if I wasn't a breeder.
The costs for those types of trips weren't a direct cost to any specific litter, but they were certainly directly related to breeding and were essentially financed by the "profit" from previous litters.
And then there are the times when breeders incur often tremendous costs and get nothing to show for it. We raised and titled a female, got her health testing done, paid a stud fee, flew her to the east coast for a breeding, paid to have her boarded there for a week, and flew her home, and she came up empty. Turned out she had ovarian cysts and was infertile. We may have incurred the same costs to train and title and health test her whether we bred her or not. We certainly wouldn't have lost more than $2000 of non-refundable stud fee and travel costs to never get any pups from her.
Purchased an adult, titled, proven broodbitch from Germany for breeding. There's $6000. Paid a stud fee and travel costs for her to go to TX to be bred. About $2500 more. Left her down there until she could be ultrasounded to confirm pregnancy and she came up empty. Left her down the until her next heat cycle, paying several hundred a month in board, to try again. No pups that time either. Instead she came home HW+ despite the fees we paid for boarding including giving her Heartguard while she was there. So then a couple grand to treat the HW. Tried breeding her one last time, this time using an AI to the tune of about $3000 more. Still no pups. Despite her having had a litter 6 months before we bought her we never were able to get her pregnant and ended up spaying her and she retired to the couch. More than $10k invested in what became just a pet.
We've tried 3 other AI breedings, both frozen and fresh chilled, usually at $3000-$4000 a pop by the time all costs are tabulated, and gotten no pups.
While we aren't the most lucky breeders on the planet when it comes to those things, our experiences are not abnormal either. I know dozens of breeders who have been through the same thing, over and over again, dumping thousands of dollars into trying to do breedings and getting no puppies to sell to recoup the costs. Those are all directly related to breeding, things we wouldn't be spending money on if we weren't breeders, and it is that little bit of "profit" from the litters that go well that makes up for those losses.