I Tag My Ex Because Of The Dog – Leo and Rebecca Buzz Question

Leo and Rebecca Buzz Question... When me and MY EX broke up I got the DOG!! But I told him that he could see him from time to time. Well, 1 year later and I have a new MAN. Well, my new MAN gets upset every time I TAG MY EX on FB whenever he has to do with the dog. My new mans says it's time to end this little ritual. Is he right?