So since we are breaking this barrier, I can marry my dog now right?
You know, what you can't seem to understand is that this is love between adult humans. The philosopher Martin Buber talks about every relationship being an "I-Thou," whereas you own a pet. You may love them, but you can't reach an "I-Thou" relationship.
Or a simpler way of thinking of it is that marriage is open only to those who can sign a contract of any kind. Dogs can't make contracts.
Now, think about a trickier issue: why are multiple marriages illegal? Why can't people have two wives or two husbands? Or more? Everybody's a free adult, right? So quick, how do you exclude harems from the right to contract?