Let's take oil as an example. Dino or mineral oil breaks down, synthetic oil does too but much less than mineral oil. When you have old oil in your car's engine, it cannot protect the internal parts as well as it should, like with fresh oil. An old oil filter will clog up eventually, so that obviously needs to be replaced. In a specific example of diesel oils, that have soot protection, the oil will degrade over time and will absorb the soot the engine produces. These particles blacken the oil, and act as microscopic abrasives, so it's like sandpaper in your engine. The longer you go without an oil change, the rougher the sand becomes, so to speak. And the protection capabilities also diminish rapidly.

The same goes with coolant, transmission fluid, power steering fluid, differential oil, ball joints (although for those you just replace the whole ball joint, but some cars had grease nipples back in the day, and had to be periodically lubricated as well), etc.

Think of it this way, would you like to drink rotten (insert liquid like milk, juice, etc)? I'm sure if your car could answer that for you it would have the exact same answer.