Uuuuuuuuum nobody was referred to as a dog. The joke implies his momma was a slut and might have fucked a dog that night....thus he's lucky he doesn't bark....in other words she didn't fuck the dog OR the dog didn't get her pregnant. Plain and simple, nobody was referred to as a dog.
I kinda hate to jump in the middle of this ridiculousness, but .....
Actually, Nuggyt ... the 'joke' can be interpreted to be saying that his momma definitely fucked a dog that night .... in addition to screwing Barack's father ... and possibly an untold number of others as well!!
To say that the son is lucky he doesn't bark merely suggests that a DOG wasn't his father!! But the inference is that she DID screw a dog that night ... amongst other things and/or people ... and that his father was one of them!!
The email is ALSO very much RACIST in nature in that it starts off discussing the differences between being "Black" and "White" ... and you'd have to be in denial (or some kind of idiot) to try to ignore that those terms are meant to describe race and people when talked about in that way in this country. A "mother" and "son" ... "Black" and "White" .... has "race" written all over it.
It wasn't the most overt or vile of racist connotations .... in fact, it was mild by many standards!! But ... it WAS a racial inference. And it DID infer that his mother was a slut AND fucked a dog - AND (at least) Barack's father that same night!! But ... she didn't have a puppy ... she had a (human) son.
If they hadn't made the "joke" personal about the President (by mentioning him by name) ... then, yeah, I can agree with you ... it would have been funny hell!!!
But .. alas .... they had to fuck it up (as they usually do ), and make it rude, racist, disrespectful and totally inappropriate!! I'll bet a month's salary that everyone he sent it to was White.