Now go and read reams of case law so you understand how the courts and CPS interpret the law.
You said there is not an offense. There is! If you meant "There is a law, but in practice I think it never gets applied" then you should say that. Really.
Just reading the legislation (and that's overview is not the legislation, it's quite a poor interpretation) won't win you any court cases.
Whereas telling the court that a law that makes something an offense does not exist is a guaranteed case winner...
You also need to read the guidelines.for prosecutor's dog.v cat incidents, which basically say its in the nature of dogs to chase cats, so a cat would not normally be considered 'an animal' for the purposes the act.
This is very strange - a few moments ago you said there was no such law, now you claim to have read prosecutors guidelines???
You are right, you're clearly not a lawyer. For criminal law there has to be mens rea, or intent. For certain pieces of criminal law 'recklessness' is sufficient.
While I agree I am not a lawyer, I think you should consider that you might be even less of one.
Concerning mens rea, you have made two mistakes:
1. There are such things as "strict liability" offenses where mens rea does not apply.
2. When an offense is defined as being a failure of duty, the only mens rea needed is the intention to fail in that duty - not to perform the actual resulting act.
For example, if you deliberately skip on airliner safety and people, then get you have committed a crime - that you didn't want them intend them to die does not remove mens rea for criminal negligence, only for murder. The law I referred to is phrased - according to the government summary - in the same way: failure of responsibility is defined as in itself cuplable.
You might not like this, but that is the law!