We have nothing in common, poodle
Referring to a woman ‘poodle’ could be a female dog = bitch.
This line is a reference to a video that went viral called “Ramen Noodle, the Wonder Poodle, and Little Orphan Juliet (Ramen is an extremely playful pup that was born without its front legs). Em is indeed using poodle as an insult to other rappers.
Again playing on the white trash line from earlier, Em is saying that other rappers are like Poodles, dressed up to look good, and rich, while he grew up poor and hard. Also, poodles are known to be very vocal dogs, but always back down in a real fight, like the rappers Em is insulting throughout the track.
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