Because alcohol, like any other drug, affects the neurotransmitters in your central nervous system. The key ingredient in alcohol, ethanol, enters your blood stream from your intestine and crosses the blood brain barrier and enters your synapses. Once its there, the ethanol increases the level of a neurotransmitter called GABA, which stands from Gamma amino butyric acid. GABA is one of the CNS, which stands for central nervous system,is one of the main inhibitory neurotransmitters, which means it increases the frequent of IPSPs, inhibitory post synaptic potentials,which reduces the number of action potentials between neurons. This basically means the neurons fire less frequently and therefore your cognition is altered because of that, I.e since your neurons are firing less action potentials, your cognition gets slowed down. This is why people sometimes do stupid things when they're drunk, they think less of their actions because they think less about the possible outcomes because neurons in the region of the brain, specifically the frontal lobe, called the prefrontal cortex becomes less active, so you are less able to the possible outcomes. And thats what anxiety basically is, your afraid of the potential outcomes if a situation and that causes fear and what's responsible for this behaviour is a bunch of neural circuits firing action potentials, every single thought you have is solely due to the communication between cells in your brain. So basically you drink alcohol, GABA levels increase and your neurons become less active-I.e they produce less action potentials and therefore neurons communicate less with one another, and that deals with anxiety because increased levels of GABA make neurons fire less, so brain becomes less active, and networks of neurons that are responsible for planning, anxiety, or even behaving properly etc.become less active. That's then biological aspect of the process, in psychology, there are other explanations, such as the social expectancy theory but I'm not very familiar with those, obviously cause its in the domain of social psychology, what people call a "soft" science, there's less hardcore evidence than the biological explanation of why alcohol makes you less inhibited. If you're interested in this stuff I'd recommend a pharmacology course or read some books on it. A good book for introduction to this stuff is Marc Lewis book memoirs of an addicted brain.