Denny moved Enzo into his apartment in Seattle, which overlooked Lake Washington. Enzo didn't enjoy living in an apartment much since he was young and used to open fields, but he liked their balcony that overlooked the lake, since he's part water dog. During the first year, Denny and Enzo formed a deep bond. Enzo was surprised, then, when Denny fell in love with Eve as fast as he did.
Enzo is still very much attached to his breeding—it's one of the ways he shapes his identity. He also builds his identity through his relationship with Denny, and this sets up both their very strong bond, and something that comes between it with the introduction of Eve.
Enzo watches Eve and Denny have sex for the first time, saying that Eve said "the field is fertile—beware!" Denny replied that he embraced the fertility. Afterwards, when Denny went to splash in the bathroom, Eve patted Enzo's head. Enzo was just over a year old, immature, and intimidated by the screaming. Eve told Enzo she wouldn't come between him and Denny. Enzo says that he respected her for saying this, but found it disingenuous because he knew she would come between them.
Again, we see Enzo's sharp perception of language and how it works. Eve presumably isn't fully aware of how much Enzo understands, but Enzo reads into her words and what they mean. He understands that her words are meant to help, but they only serve to create a rift between Eve and Enzo.
Enzo says that he tried to act nonchalant because he knew how much Denny loved Eve, but he wasn't embracing of her presence. In turn, Eve was less embracing of Enzo. Enzo describes them as satellites orbiting Denny, struggling for supremacy, although Eve had the advantage of a tongue and thumbs. Sometimes she would wink at Enzo as if to gloat about her physical advantage in their battle.
Here the rift between Enzo and Eve is brought to the forefront. Notice that it's not just about language for Enzo, it's about Eve's humanity allowing her to triumph in their battle for Denny's affection. Enzo's love for Denny, however, keeps it from being overly hostile.