I think it is the same reason people become addicted to anything. At first it may distract them from their problems. However, unless you solve the real issues, it won't help for long. Next, your body gets used to it and makes real changes in your brain and body to deal with all the toxins, since alcohol is really a poison and the body has to detoxify it to keep you alive.
The byproducts of the alcohol detoxification process are what make people feel different after drinking. However, this comes with a big price. Eventually, you will feel much worse than you did before drinking alcohol, so people start drinking just to feel normal again.
You will often see people who drink or take drugs having all kinds of problems when they stop, like arm shaking and other discomfort, so they have to keep drinking to relieve it. It eventually destroys their liver and other organs and leads to death if they can't stop, which is very sad.