It is a good bet most of what you think about tannins in wine is wrong.
On the evolutionary level, wine tannin plays a healing and defense role for vines. Tannins break down proteins, discouraging herbivores, and also help cut or wounded plants heal. In a sense, wine vine tannins are similar to clotting agents in your blood.
In our mouths, tannins are astringent, meaning they dry out your mouth. Often wine tannins are compared to tea, which also is tannic, but they also can be compared to a dentist holding your tongue with gauze. The key is the drying effect.
That effect is why tannic wines work so well with rich red meats or other fatty, protein-rich foods. Much the way acidic white wines cleanse the palate and set your palate up for the next bite of seafood or salad, tannic red wines set your palate up for the next bite of umami-centered food.
Tannin’s protective role also is critical in making red wines capable of astonishing aging. The more tannic the wine, the longer it can age. Really age. There are special red wines that are deliriously wonderful at age 100 and more.
Tannins come from various parts of the grape, some are exquisite, some not so much. The first source are grape skins, with red grapes providing more than white. Seed tannins are not really tannins, but close enough they are lumped together. Cheap wines made from heavily-pressed grapes—which cracks seeds—floridly flaunts these harsh tannins, which is why such wines add sugar to make them sweeter to mask the tannins. That and other cheap wine tricks contribute to your blinding hangover the next morning.
Oak provides tannins, although thankfully not as assertively as seed tannins. Oak tannins are most flamboyant in new oak barrels, especially new American oak, but mercifully these blow off with decanting.
People claim tannins cause headaches. They do not; drinking too much tannic wine is the cause. People claim they are allergic to tannins; maybe, you can find people allergic to almost anything, but it is not common. You may not like the drying sensation found in red wine. Fine. Drink white and rosé while the rest of us slurp a red while enjoying a well-marbled slab of steak.
Last round: Someone told me I did not need to drink wine to make myself more fun to be with. I told him I was drinking wine to make him more fun to be with.