I don't think we can say ever but there are factors that may inhibit transfer of disease both ways.
In order to understand how zoonotic infection we can look at a possible scenario for how SARS-CoV-2 appeared. One possiblity is that bats were housed in close proximity to pangolins in South China. The bats passed the virus to the pangolins who likely mutated the virus to a point it was able to transmit it to humans. Pangolins are insect eaters and could easily eat some bat dung. There are reports of sick pangolins that died with a pneuonia like illness in Guangzhou rescue centres at the approximate time of the genetic origin of the virus.
Once inside humans it likely spent sometime mutating further before it became the A ancestral variant discovered in Guangzhou and the USA. This then mutated to become the B variant found in Wuhan.
The virus being a RNA virus mutates very rapidly. But to remain infective it has to have a high affinity for the ACE2 receptor, and variants of this receptor are found in the mammalian kingdom. Ferrets and cats have ACE2 receptors closely related to human ACE2 and there are reports that felines have been infected in zoos and homes. However, the disease in other animals may not be as severe as in humans due to differences in ACE2, and immune systems, and although they may get the virus it may not be as severe an illness so they might not excrete enough virus to then reinfect humans.