People had no problem starting clinics in the past and they probably could today if they really wanted to, but there is little incentive to for the past few decades while the stock market has been booming. Why spend 80 hours a week struggling to run your own clinic and paying off loans when you can work 40 hours a week working for somebody else's clinic and invest your savings in the stock market?

Find an investor.

Could a veterinary business not be bootstrapped?

Assuming you had $$$ for some supplies but couldn't afford to lease a commercial building, you could provide small mammal services from your vehicle, driving to people's homes to give vaccinations and well care.

Being mobile would also allow you to serve a larger market than a fixed clinic; you could serve a couple small towns on Monday, a couple others on Tuesday, and server a larger metro on the weekends.

Once you're consistently profiting $$$$/day you'll be able to start saving for the equipment you'll need for a commercial lease somewhere because you have both the cash, cash flow, a loyal customer base, and critically, a good sense of where a good location would be to serve them from.