Cat identifies as a dog

 Here's a description of the issue:

Our home owners association (HOA)fees include a play area for dogs, except to gain access to that sanctuary one must purchase a key-card.  It’s a proximity device that causes the electronic gate latch to admit a person and his “dog” when the card is held near the latch.  One might object to my use of the word “his” in the previous sentence, but it seems to me that it’s a bit more precise than the pronoun “their” since it refers to a single individual, or implies such.

So, here’s the problem.  Our HOA is unwilling to sell me a key-card to that “dog” sanctuary since one of the board members learned I want to use the exercise area for play with my cat.  I’ve already explained to them that our cat truly identifies as a dog.  Our cat’s name is Tom and he acts like he’s really a dog.  That guy will attack on command.  He will fetch a tossed ball and return it immediately, dropping on the ground in front of me eager to repeat the exercise.  One of my problems is that our yard is too small to toss the ball any great distance, but the so-called dog area is huge where exercises of “fetch” are unlimited.  Additionally, Tom runs to our driveway each morning and grabs up the daily newspaper and brings it to me, just like our dog Spot used to do before he went to wherever dead dogs go. . He drops it on the floor directly in front of me, but doesn’t expect me to toss it for a fetching exercise.  Tom knows the difference.  However, he doesn’t know what a cat really is,  you see, he’s not a cat in his feline mind, he’s a dog.  

It’s also puzzling to me that all of the HOA board members fail to understand the issue.  In fact, one of the board members is a transgender person who should clearly understand my problem and vote in my favor.  Do you agree?