I have a friend who was told by his EC that he could not have his small dogs in his apartment. The reason was because they are there. There has been no complaints, no incidents within the complex. It is just because one EC member saw the dogs going for a walk. He took it to mediation nd then the tribunal and he won.
Have.a look at the pets in the city website. It has a lot of information about pets in strata. Also, the law society website has a section about pets in strata. If you re friendly with any other owners you could talk to them as to whether they are bothered by the fact you have a cat.
I believe it is unreasonable to deny permission for a pet simply because it is there. If they do not want pets in their complex they should have had that written into the by laws.