You speak more fluently on alcohol because after the initial spike in dopamine, it actually floods your brain with GABA, which is an inhibitory neurotransmitter that essentially puts the brakes on excitatory neurotransmitters like dopamine and glutamate etc…. This relaxes the central nervous system and muscles, and the temporary result is smoother, fluent speech. When the intoxicating effects of alcohol & GABA wears off, the rebound of dopamine results in the dysregulation and hyperactivity in the speech-motor networks again, and you begin to stutter again (sometimes even more the next day).