Don't get me wrong, the image is totally unfair.

I'm only objecting to the "it sounds a lot like dating someone because you plan to 'fix them'" because cats are usually misunderstood. They have their own body language, which is very different and sometimes opposite to that of dogs.

So saying "I don’t like cats because they remind me of shitty people I’ve dated" reads to me like you probably don't understand how they're communicating with you, and you're accidentally crossing some boundaries.